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S I 



LESSONS IN ASTRONOMY 

INCLUDING URA1STOGRAPHY 

A BRIEF INTRODUCTORY COURSE 
WITHOUT MATHEMATICS 

BY 
CHARLES A. YOUNG, Ph.D., LL.D. 

Professor of Astronomy in Princeton University, Author of 

a " General Astronomy for Colleges and Scientific 

Schools," of a "Manual of Astronomy," and 

of "Elements of Astronomy" 



REVISED EDITION 



. e " v -> 



Boston, U.S.A., and London 

GINN & COMPANY, PUBLISHERS 

©be athenaeum JJresa 

1903 



the library of 

CCNoKbSS. 


Two Copies Received 


APR 15 io{)3 


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CLASS «/ XXe. No 

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COPY B. ' 



Entered at Stationers' Hall 



Copyright, 1895, 1903 
By .CHARLES A . YOUNG 

ALL RIGHTS RESERVED 



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PREFACE TO THE ORIGINAL EDITION 



This volume has been prepared to meet the want of 
certain classes of schools which find the author's " Elements 
of Astronomy " rather too extended and mathematical to 
suit their course and pupils. It is based upon the Ele- 
ments, but with many condensations, simplifications, and 
changes of arrangement: everything has been carefully 
worked over and rewritten in order to adapt it to those 
whose mathematical attainments are not sufficient to enable 
them to use the larger work to advantage. 

Of course, such pupils cannot gain the same insight into 
the mechanism of the heavens as those who take up the 
subject at a more advanced stage in their education. They 
must often be contented with the bare statement of a fact 
without any explanation of the manner in which its truth 
is established, and thus will necessarily miss much that is 
most valuable in the discipline to be derived from the study 
of Astronomy. 

But enough remains — surely there is no other science 
which, apart from all questions of How or Why, supplies 
so much to widen the student's range of thought and to 
make him comprehend his place in the infinite universe. 

The most important change in the arrangement of the 
book has been in bringing the Uranography, or " constella- 
tion-tracing," into the body of the text and placing it near 



iv PREFACE 

the beginning, — a change in harmony with the accepted 
principle that those whose minds are not mature succeed 
best in the study of a new subject by beginning with what 
is concrete and appeals to the senses, rather than with the 
abstract principles. It has been thought well also to add 
brief notes on the legendary mythology of the constellations 
for the benefit of such pupils as are not likely to become 
familiar with it in the study of classical literature. 

In the preparation of the book great pains have been 
taken not to sacrifice accuracy and truth to compactness, 
and no less to bring everything thoroughly down to date. 

The Appendix contains in its first chapter descrip- 
tions of the most used astronomical instruments, and where 
time permits, might profitably be brought into the course. 
The second chapter of the Appendix is designed only 
for the use of teachers and the more advanced pupils. 
Sees. 431-434, however, explaining how the sun's dis- 
tance may be found in the simplest way, might well be 
read by all. 



1891. 



PREFACE TO THE REVISED EDITION 



Since the original publication of this work twelve years 
ago, a number of editions have been issued in which it was 
attempted to keep up to date, as far as possible, by such 
minor changes and corrections as typographical considera- 
tions would permit. It has now, however, seemed best to 
reprint the book from entirely new plates, and this has 
given an opportunity for a thorough revision of the work 
and the free introduction of all desirable improvements 
and additions. The former rather unsatisfactory star-maps 
have been replaced by new ones, and a considerable number 
of beautiful half-tone illustrations have been added. 

The publishers have spared no pains or expense in the 
mechanical execution of the volume, and it is hoped that, 
so far as its scope permits, the book will now be found 
to offer a satisfactory summary of the present state of 
Astronomy. 

C. A. YOUNG. 

Pkinceton, N.J., 
January, 1903. 



CONTENTS 



CHAPTER I. [introduction Fundamental Notions 
and Definitions The Celestial Sphere and its Circles 
A it it ikIc .- i i m l Azimuth Right Ascension and Dec- 
lination Celestial Latitude and Longitude . . 11!) 

CHAPTER II. UltANOtiltAI'IIY (ilohcs ;ni(l Slat Maps 

Star Ma^nituilrH Names ;in<l Designations of 
stars The Constellations in Detail .... 20 68 

CHAPTER in. Fundamental Problems Latitude 

and the Aspect of the Celestial Sphere Time, Lon 

gitude, and the Place of a Heavenly Body . . . 64 77 

CHAPTER IV. The Earth [ts Form and Dimen 

sioiis; its Rotation, Mass, ami Density Its Orbital 
Motion and I lie Seasons Preeession The Year and 
fche Calendar 78 L04 

CHAPTER v. The Moon Her Orbital Motion and 
bhe Month Distance, Dimensions, Mass, Density, and 

Force of (h;i\ it y Potation and Lilnaiions Phases 

Light and Heat Physical Condition Telescopic 
Aspect and Surface 105 L28 

CHAPTER VI. The Sun Its Distance, Dimensions, 

MaSS, and Density Its Potation, Surface, and Spots 
— The Spectroscope and the Solar Spectrum The 

Chemical Constitution of the Sun The Chromosphere 
and Prominences The Corona The Sun's Light 

Measurement and Intensity of the Sun's Heat 
Theory of its Maintenance and specula t ions regarding 
the Age and Duration of the Sun ... 129 L70 

vii 



viii CONTENTS 

PAGES 

CHAPTER VII. — Eclipses and the Tides — Form and 
Dimensions of Shadows — Eclipses of the Moon — 
Solar Eclipses, Total, Annular, and Partial — Number 
of Eclipses in a Year — Recurrence of Eclipses and 
the Saros — Occultations — The Tides . . . 171-187 

CHAPTER VIII. — The Planetary System — The Plan- 
ets in General — Their Number, Classification, and 
Arrangement — Bode's Law — Orbits of the Planets 

— Kepler's Laws and Gravitation — The Apparent 
Motions of the Planets and the Systems of Ptolemy 
and Copernicus — Determination of the Planets' Diam- 
eters, Masses, etc. — Herschel's Illustration of the 
System — Description of Individual Planets — The 

< Terrestrial ' Planets, Mercury, Venus, and Mars . 188-224 

CHAPTER IX. — Planets (Continued) — The Asteroids 

— Intramercurian Planets and the Zodiacal Light — 
The Major Planets, Jupiter, Saturn, Uranus, and 
Neptune — Ultra-Neptunian Planet .... 225-251 

CHAPTER X. — Comets and Meteors — Comets, their 
Number, Designation, and Orbits — Their Constituent 
Parts and Appearance — Their Spectra, Physical Con- 
stitution, and Probable Origin — Remarkable Comets 

— Photography of Comets — Aerolites, their Fall and 
Characteristics — Shooting-Stars and Meteoric Showers 

— Connection between Meteors and Comets . . 252-293 

CHAPTER XL — The Stars — Their Nature, Number, 
and Designation — Star-Catalogues and Charts — Their 
Proper Motions and the Motion of the Sun in Space 

— Stellar Parallax — Star Magnitudes and Photometry 

— Variable Stars — Stellar Spectra .... 294-325 

CHAPTER XII. — The Stars (Continued) —Double and 
Multiple Stars — Clusters and Nebulae — The Milky 
Way and Distribution of Stars in Space — The Stellar 
Universe — Cosmogony and the Nebular Hypothesis . 326-357 



L 



CONTENTS ix 



APPENDIX 

PAGES 

ASTRONOMICAL INSTRUMENTS. — The Telescope, 
Simple Refracting, Achromatic, and Reflecting — The 
Equatorial — The Filar Micrometer — The Transit- 
Instrument — The Clock and the Chronograph — The 
Meridian Circle — The Sextant ..... 359-378 

MISCELLANEOUS (for the most part supplemen- 
tary to articles in the text). — Hour- Angle and 
Time — Twilight — Determination of Latitude — Place 
of a Ship at Sea — Finding the Form of the Earth's 
Orbit — The Ellipse — Illustrations of Kepler's " Har- 
monic " Law — The Equation of Light and the Sun's 
Distance determined by it — Aberration of Light — 
De ITsle's Method of getting the Sun's Parallax from a 
Transit of Venus — The Parabola and the Conic Sec- 
tions — Determination of Stellar Parallax . . . 378-397 

QUESTIONS FOR REVIEW 398-400 

TABLES OF ASTRONOMICAL DATA 

I. Astronomical Constants ..... 401 

II. The Principal Elements of the Solar System . 402 

III. The Satellites of the Solar System . . . 403 

IV. The Principal Variable Stars .... 404 
V. The Best Determined Stellar Parallaxes . . 405 

The Greek Alphabet and Miscellaneous Symbols . 406 

IXDEX 407-420 

STAR-MAPS 



LESSORS EST ASTRONOMY 



CHAPTER I 

INTRODUCTION 

Fundamental Notions and Definitions — The Celestial Sphere and its Circles 
— Altitude and Azimuth — Right Ascension and Declination — Celestial 
Latitude and Longitude 

1. Astronomy 1 is the science which deals with the 
heavenly bodies. 

As it is the oldest of the sciences, so also it is one of the 
most perfect, and in certain aspects the noblest, as being 
the most " unselfish " of them all. And yet, although not 
bearing so directly upon the material interests of life as 
the more modern sciences of Physics and Chemistry, it is 
of high utility. 

By means of Astronomy the latitudes and longitudes of 
places upon the earth's suface are determined, and by such 
determinations alone is navigation made secure. More- 
over, all the operations of surveying upon a large scale, 
such as the determination of national boundaries, depend 
more or less upon astronomical observations. The same 
is true of operations which, like the railway service, require 
an accurate knowledge and observance of time ; for the 
fundamental timekeeper is the diurnal revolution of the 
heavens. 

1 The term is derived from two Greek words : astron (a heavenly body) 
and nomos (a law). 

1 



2 LESSONS IN ASTRONOMY 

In ancient times the science was supposed to have a still higher 
utility. It was believed that human affairs of every kind, the wel- 
fare of nations, and the life history of individuals alike, were con- 
trolled, or at least prefigured, by the motions of the stars and planets ; 
so that from the study of the heavens it ought to be possible to pre- 
dict futurity. Hence originated the pseudo-science of Astrology, 
which, baseless and absurd as it has been proved to be, still retains 
a remarkable hold on the popular mind. 

2. The heavenly bodies include, first, the solar system, 
— that is, the sun and the planets which revolve around 
it, with their attendant satellites ; second, the comets and 
the meteors, which also move around the sun, but are 
bodies of a very different nature from the planets and 
travel in different orbits ; and, third, the stars and nebulae. 
The earth on which we live is one of the planets, and 
the moon is the earth's satellite. The stars which we see 
are bodies of the same kind as the sun, shining like him 
with fiery heat, while the planets and the satellites are 
dark and cool like the earth and visible only by the sun- 
light they reflect. As for the comets and nebulae, they 
appear to be mere clouds, composed of gas or swarms 
of little particles, perhaps not very hot, but luminous. 
It is likely, practically certain indeed, that besides the 
visible stars there are also multitudes of others too cool 
to shine, some of which manifest their existence by 
affecting the motion of certain of the visible stars. It is 
hardly necessary to add that while with the naked eye 
we see only a few thousand stars, the telescope reveals 
millions. 

3. As we look off from the earth at night, the stars 
appear to be all around us, like glittering points fastened 
to the inside of a huge hollow globe. Really they are at 



INTRODUCTION 3 

very different distances, all enormous as compared with 
any distances with which geography makes us familiar. 
Even the moon is eighty times as far away as New York 
from Liverpool, and the sun is nearly four hundred times 
as distant as the moon, and the nearest of the stars is 
nearly three hundred thousand times as distant as the sun ; 
as to the remoter stars, some of them are certainly thou- 
sands of times as far away as the nearer ones, — so far 
that light itself is thousands of years in coming to us from 
them. These are facts which are certain, not mere guesses 
or beliefs. 

Then, too, as to their motions. Although most of the 
heavenly bodies seem to us to be at rest, except as the 
earth's rotation makes them appear to rise and set, yet 
really they are all moving, and with a swiftness of which 
we can form no conception. A cannon-ball is a snail com- 
pared with the slowest of them. The earth itself in its 
revolution around the sun is flying eighteen and a half 
miles in a second, which is more than fifty times as fast as 
the swiftest rifle bullet. We fail to perceive the motion 
simply because it is so smooth and so unresisted. The 
space outside our air contains nothing that obviously 
obstructs either sight or motion. 

4. But this knowledge as to the real distance and 
motions of the heavenly bodies was gained only after 
long centuries of study. If we go out to look at the stars 
some moonless night, we find them apparently sprinkled 
over the dome of the sky in groups, or constellations, which 
are still substantially the same as in the days of the earliest 
astronomers. At first these constellations were figures of 
animals and other objects, and many celestial globes and 



4 LESSONS IN ASTRONOMY 

maps still bear grotesque pictures 1 representing them. At 
present, however, a constellation is only a certain region 
of the sky, limited by imaginary lines which divide it 
from the neighboring constellations, just as countries are 
divided in geography. As to the exact boundaries of these 
constellations, and even their number, there is no precise 
agreement among astronomers. Forty-eight of them have 
come down to us from the time of Ptolemy (the greatest 
astronomer of antiquity, who flourished at Alexandria about 
a.d. 130), and even in his day many of them were already 
ancient. 

About twenty others, proposed by later astronomers, are 
now generally recognized, and at least as many more have 
been suggested and abandoned. 

5. Uranography, or Description of the Visible Heavens. — 
The study of the constellations, or the apparent arrange- 
ment of the stars in the sky, is called Uranography. 2 It 
is not an essential part of Astronomy, but it is an easy and 
pleasant study; and in becoming familiar with the con- 
stellations and their principal stars the pupil will learn 
more readily and thoroughly than in any other way the 
most important facts in relation to the apparent motions 
of the heavenly bodies, and the principal points and 
circles of the celestial sphere. For this reason the teacher 
is urged to take the earliest opportunity to have his 
pupils trace such of the constellations as happen to be 
visible in the evening sky when they begin the study of 
Astronomy, and to continue it from time to time as the 
progress of the seasons gives opportunity. 

1 Most of these figures follow the designs of Albert Diirer. 

2 From the Greek, ouranos (heavens) and graphe (description). 



INTRODUCTION 5 

6. The Celestial Sphere. 1 — The sky appears like a hollow 
vault, to which the stars seem to be attached like specks 
of gilding upon the inner surface of a dome. We cannot 
judge of the distance of this surface from the eye, further 
than to perceive that it must be very far away. It is there- 
fore natural and extremely convenient to regard the dis- 
tance of the sky as everywhere the same and unlimited. 
The celestial sphere, as it is called, is conceived of as so 
enormous that the whole world of stars and planets lies 
in its center like a few grains of sand in the middle of 
the dome of the Capitol. Its diameter is assumed to be 
immeasurably greater than any actual distance known, 
and greater than any quantity assignable. In technical 
language it is taken as infinite. 

Since the celestial sphere is thus infinite, any two 
parallel lines drawn from distant points on the surface of 
the earth, or even from points as distant as the earth and 
the sun, will seem to meet at one point on the surface of the 
sphere. If the two lines were anywhere a million miles 
apart, for instance, they will, of course, still be a million 
miles apart when they reach the surface of the sphere ; 
but at an infinite distance even a million miles is a mere 
nothing, so that, to our observation, the two lines are close 
together and make apparently but a single point 2 where 
they pierce the sphere. 

7. The Apparent Place of a Heavenly Body. — This is 
simply the point where a line drawn from the observer 

1 The study of the celestial sphere and its circles is greatly facilitated 
by the use of a globe, or armillary sphere. Without some such apparatus 
it is not easy for a young person to get clear ideas upon the subject. 

2 This is the same as the "vanishing point" of perspective. 



LESSONS IN ASTRONOMY 



through the body in question, continued outward, pierces 
the celestial sphere. It depends solely upon the direction 
of the body, and is in no way affected by its distance from 
us. Thus, in Fig. 1, J, B, C, etc., are the apparent places 
of a, 6, e, etc., the observer being at 0. Objects that are 
nearly in line with each other, however great the real dis- 
tances between them, as A, i, &, will appear close together 
in the sky. The moon, for instance, often looks to us 

" very near" a star, which 
is really of course at an 
enormous distance beyond 
her. 

8. Angular Measurement. 
— It is clear that we cannot 
properly describe the appar- 
ent distance of two points 
upon the celestial sphere from 
each other by feet or inches. 
To say that two stars are 
about five feet apart, for in- 
stance, — and it is not very uncommon to hear such an 
expression, — means nothing unless we know how far from 
the eye the five-foot measure is to be held. The proper 
units for expressing apparent distance in the sky are those 
of angle, viz.: degrees (°), minutes ('), and seconds ("); the 
circumference of a circle being divided into 360 degrees, 
each degree into 60 minutes, and each minute into 60 
seconds. Thus, the Great Bear's tail, or " Dipper-handle," 
is about 16° long, and the long side of the " Dipper-bowl " 
is about 10°; the moon and the sun are each about half a 
degree, or 30', in diameter. 




Fig. i 



INTRODUCTIOX 7 

It is very important that the student in Astronomy should become 
accustomed as soon as possible to estimate celestial measures in this 
way. A little practice soon makes it easy, though at first one is apt 
to be embarrassed by the fact that the sky looks to the eye not like 
a true hemisphere but like a flattened vault, so that the estimates of 
distances for all objects near the horizon are apt to be too large. 
The moon, when rising or setting, looks to most persons much larger 
than when overhead ; l and the Dipper-bowl, when underneath the 
pole, seems to coyer a much larger area than when above it. 

9. Circles and Principal Points of the Celestial Sphere. — 

Just as the surface of the earth in Geography is covered 
with a network of imaginary lines, — meridians and par- 
allels of latitude, — so the sky is supposed to be marked 
off in a somewhat similar way. Two such sets of points 
and reference circles are in common use to describe the 
apparent places of the stars, and a third was used by the 
ancients and is still employed for some purposes. The first 
system depends upon the direction of the force of gravity 
shown by a plumb-line at the point where the observer 
stands ; the second upon the direction of the axis of the 
earth, which points very near to the so-called Pole-star; 
and the third depends upon the position of the orbit in 
which the earth travels around the sun. 

10. The Gravitational or Up-and-Down System. — (a) The 
Zenith and Nadir. The point in the sky directly above 
the observer is called the zenith; the opposite point, under 
the earth and of course invisible, the nadir? 

1 This is a pure illusion due to physiological causes affecting judg- 
ment of distance and size. The moon at the horizon is really about 
4000 miles more distant from the observer than when nearly overhead, 
and its apparent diameter, as measured by an astronomical instrument, is 
actually less by about one-thirtieth. 

2 These are Arabic terms. About a.d. 1100 the Arabs were the world's 



8 LESSOXS IX ASTRONOMY 

(b) The Horizon (pronounced ho-ri'-zon, not hor'-i-zon). 
This is a " great circle "* around the sky, half-way between 
the zenith and the nadir, and therefore everywhere 90° 
from the zenith. The word is derived from a Greek word 
which means a " boundary"; i.e., the line where the earth 
or sea limits the sky. The actual line of division, which 
on the land is always more or less irregular, is called the 
visible horizon, to distinguish it from the true, or astro- 
nomical, horizon defined above. 

We may also define the horizon as the great circle where 
a plane which passes through the observer's eye perpen- 
dicular to the plumb-line cuts the celestial sphere. 

11. Vertical Circles and the Meridian ; Altitude and Azi- 
muth. — Circles drawn from the zenith to the nadir cut the 
horizon at right angles, and are known as vertical circles. 
Each star has at any moment its own vertical circle. 

That particular vertical circle which passes north and 
south is known as the Celestial Meridian ; while the ver- 
tical circle at right angles to this is called the prime vertical. 
Small circles drawn parallel to the horizon are known as 
parallels of altitude, or almucantars. Fig. 2 illustrates these 
definitions. 

By their help we can easily define the apparent position 
of a heavenly body. 

Its Altitude is its apparent elevation above the horizon ; 
that is, the number of degrees between it and the horizon, 
measured on a vertical circle. Thus, in Fig. 2, the 

chief astronomers, and have left their mark upon the science in numerous 
names of stars and astronomical terms. 

1 "Great Circles' ' are those which divide the sphere into two equal 
parts. 



INTRODUCTION 9 

vertical circle ZJIR passes through the point M. The arc 
J///, measured in degrees, is the altitude of Jf, and the 
arc ZJI is called its zenith distance. 

The Azimuth of a heavenly body is the same as its 
" bearing " in Surveying, but measured from the true 
meridian and not from the magnetic. 1 It is the arc of 
the horizon, measured in degrees, intercepted between the 




Fig. 2. — The Horizon and Vertical Circles 



O, the place of the observer. 
OZ, the observer's vertical. 
Z, the zenith ; P, the pole. 
SJVXE, the horizon. 
SZPX, the meridian. 
EZW, the prime vertical. 



M, some star. 

ZMH, arc of the star's vertical circle. 

TMR, the star's alnmcantar. 

Angle TZM, or arc SH, star's azimuth. 

Arc HM, star's altitude. 

Arc ZM, star's zenith-distance. 



south point and the foot of the vertical circle which passes 
through the object. 

There are various ways of reckoning azimuth. Many 
writers express it in the same way as the " bearing" in 
Surveying, i.e., so many degrees east or west of north or 
south. In the figure, the azimuth of M thus expressed 
is about #, 50° E. The more usual way at present is, 

1 The reader is reminded that the magnetic needle hardly anywhere 
points exactly north. Its direction varies widely at different parts of the 
earth, and, moreover, is continually changing to some extent. 



10 LESSONS IN ASTRONOMY 

however, to reckon clear around from the south, through 
the west, to the point of beginning. Expressed in this 
way, the azimuth of M would be about 310°, — Le., the 
arc SWNEH. 

Altitude and azimuth, however, are inconvenient for 
many purposes, because they continually change for a 
celestial object as it apparently moves across the sky. 

12. The Apparent Diurnal Rotation of the Heavens. — 
If we go out on some clear evening in the early autumn, 
say about 8 p.m. on the 22d of September, and face the 
north, we shall find the appearance of that part of the 
heavens directly before us substantially as shown in Fig. 3. 
In the north is the constellation of the Great Bear (Ursa 
Major), characterized by the conspicuous group of seven 
stars known as the " Great Dipper." It now lies with its 
handle sloping upward to the west. The two eastern- 
most stars of the four which form its bowl are called the 
" Pointers," because they point to the Pole-star, which is 
a solitary star not quite half-way from the horizon to the 
zenith (in the latitude of New York), and about as bright 
as the brighter of the two Pointers. 

High up on the opposite side of the Pole-star from the 
Great Dipper, and at nearly the same distance, is an 
irregular zigzag of five stars, each about as bright as the 
Pole-star itself. This is the constellation of Cassiopeia. 

If now we watch these stars for only a few hours, we 
shall find that while all the forms remain unaltered, their 
places in the sky are slowly changing. The Great Dipper 
slides downward towards the north, so that by eleven o'clock 
(on September 22) the Pointers are directly under the 
Pole-star. Cassiopeia still keeps opposite, however, rising 



INTRODUCTION 



11 



towards the zenith ; and if we continue the watch through 
the whole night, we shall find that all the stars appear to 
be moving in circles around a point near the Pole-star, 
revolving in the opposite direction to the hands of a watch 




Fig. 3. — The Northern Circumpolar Constellations 



(as we look towards the north) with a steady motion which 
takes them completely around once a day, or, to be more 
exact, once in 23 h 56 m 4 s .l of ordinary time. They behave 



12 



LESSONS IN ASTRONOMY 



just as if they were attached to the inner surface of a huge 
revolving sphere. 

Instead of watching the stars by the eye we may advan- 
tageously employ photography. A camera is pointed up 
towards the Pole-star and kept firmly fixed while the stars 

by their diurnal 
motion impress 
their "trails" upon 
the plate. Fig. 4 
was made in this 
way with an ex- 
posure of about 
three hours. 

To indicate the 
position of the stars 
as it will be at mid- 
night of September 22, 
the figure must be 
held so that XII in 
the margin is at the 
bottom ; at 4 a.m. the 
stars will have come to the position indicated by bringing XVI 
to the bottom, and so on. But at eight o'clock on the next night 
we shall find things very nearly in their original position. 

If instead of looking toward the north we now look 
southward, we shall find that in that part of the sky also 
the stars appear to move in the same kind of way. All 
that are not too near the Pole-star rise somewhere in the 
eastern horizon, ascend obliquely to the meridian, and 
descend to their setting at points on the western horizon. 
The next day they rise and set again at precisely the same 
points, and the motion is always in an arc of a circle, called 




Fig. 4. — Polar Star Trails 



INTRODUCTION 13 

the star's diurnal circle, the size of which depends upon its 
distance from the pole. Moreover, all of these arcs are 
strictly concentric. 

The ancients accounted for these fundamental and obvious 
facts by supposing that the stars are really fastened to the 
celestial sphere, and that this sphere really turns daily in 
the manner indicated. According to this view there must 
really be upon the sphere two opposite points which remain 
at rest, and these are the poles. 

13. Definition of the Poles. — The Poles, therefore, may 
be defined as those two points in the sky where a star would 
have no diurnal motion. The exact position of either pole 
may be determined with proper instruments by finding the 
center of the small diurnal circle described by some star 
near it, as, for instance, by the Pole-star. 

This definition of the pole is that which would be given 
by one familiar with the sky but ignorant of the earth's 
rotation, and it is still perfectly correct ; but knowing, as 
we now do, that this apparent revolution of the celestial 
sphere is due to the real spinning of the earth on its axis, 
we may also define the poles as the two points ivhere the 
earth's axis of rotation, produced indefinitely, would pierce 
the celestial sphere. 

Since the two poles are diametrically opposite in the sky, only one 
of them is usually visible from any given place. Observers north 
of the earth's equator see only the north pole, and vice versa for 
observers in the southern hemisphere. 

The student must be careful not to confound the Pole 
with the Pole-star. The pole is an imaginary point ; the 
Pole-star is only that one of the conspicuous stars which 



14 



LESSONS IN ASTRONOMY 



happens 1 now to be nearest to that point and at present is 
about 1£° distant from it. If we draw an imaginary line 
from the Pole-star to the star Mizar (the one at the bend 
of the Dipper-handle), it will pass almost exactly through 
the pole itself ; the distance of the pole from the Pole-star 

(often called Polaris) being 
very nearly one quarter of 
the distance between the two 
"Pointers." 

14. The Celestial Equator, 
or Equinoctial ; Declination. — 
The Equator is a great circle 
of the celestial sphere drawn 
half-way between the poles, 
everywhere 90° from each of 
them, and is the great circle 
in which the plane of the 
earth's equator cuts the celes- 
tial sphere. It is often 
called the Equinoctial. Fig. 5 shows how the plane of the 
earth's equator produced far enough would mark out such 
a circle in the heavens. 

Small circles drawn parallel to the equinoctial, like the 
parallels of latitude on the earth, are known as Parallels 
of Declination, the Declination of a star being its distance 
in degrees north or south of the celestial equator ; + if north, 
— if south. It corresponds precisely with the latitude of 
a place on the earth's surface ; but it cannot be called 
" celestial latitude," because that term has been preoccupied 
by an entirely different quantity (Sec. 20). 

i See Sec. 126. 




Fig. 5. — The Plane of the Earth's 
Equator produced to cut the Celes- 
tial Sphere 



INTRODUCTION 15 

A star's parallel of declination is identical with its 
diurnal circle. 

15. Hour-Circles. — The great circles of the celestial 
sphere which pass through the poles like the meridians on 
the earth, and are therefore perpendicular to the celestial 
equator, are called Hour- Circles. Some writers call them 
" celestial meridians," but the term is objectionable since 
it is sometimes used to indicate an entirely different set of 
circles. 

That particular hour-circle which at any moment passes 
through the zenith of course coincides with the celestial 
meridian already defined in Sec. 11. 

16. The Celestial Meridian and the Cardinal Points. — 
The best definition of the celestial meridian is, however, 
the great circle which passes through the zenith and the poles. 
The points where this meridian cuts the horizon (the circle 
of level) are the north and south points, and the east and 
west points of the horizon lie half-way between them, the 
four being known as the " Cardinal Points." The student 
is especially cautioned against confounding the north point 
with the north pole. The north point is on the horizon; 
the north pole is high up in the sky. 

In Fig. 6, P is the north celestial pole, Z is the zenith, 
and SQZPN is the celestial meridian. P and P' are the 
poles, PmP ! is the hour-circle of m, and amRb V is its par- 
allel of declination, or diurnal circle. JSf and S are the 
north and south points respectively. In the figure, mY is 
the declination of m, and mP is called its polar distance. 

The angle made at the celestial pole between the merid- 
ian and the hour-circle passing through a given star is 
called the star's Hour-Angle for that moment. It is 



16 



LESSONS IX ASTRONOMY 



usually reckoned westward from the meridian, and, for many 
purposes, in time instead of in arc, i.e., in hours, minutes, 
and seconds of time instead of decrees, etc. One hour 
= 15°, and one minute of time (l m ) =15 minutes of arc 
(15% etc. The hour-angle of a star is always equal to the 



B? 




Fig. 6. — Equator, Hour-Circles, etc. 



0. place of the observer ; Z. his zenith. 

S IITF. the horizon. 

POP . line parallel to the axis of the 
earth. 

P and P . the two poles of the heavens. 

EQWTi the celestial equator, or equi- 
noctial. 

X, the vernal equinox, or "first of 
Aries." 

PXP. the equinoctial colnre. or zero 
hour-circle. 



m. some star. 

Ym. the star's declination; Pm, its 
north-polar distance. 

Angle mPP = arc QY. the star's east- 
ern) hour-angle ; = 24^ minus star's 
western hour-angle. 

Angle XPm=arc AT. star's rig Jit 
ascension. 

Sidereal time at the moment = 2-^ minus 
XPQ. 



interval of sidereal time (see Sec. 91) elapsed since the 
star last crossed the meridian. 

17. The Vernal Equinox, or First of Aries. — In order to 
use this system of circles as a means of designating the 
places of stars in the sky, it is necessary to fix upon some 
one hour-circle, to be reckoned from in the same way that 



INTRODUCTION 17 

the meridian of Greenwich is used in reckoning longitude 
on the earth's surface. The " Greenwich of the sky ,? 
which has thus been fixed upon is the point where the 
sun crosses the celestial equator in the spring. The sun 
and moon and the planets do not behave as if they, like 
the stars, were firmly fixed upon the celestial sphere, but 
rather as if they were glow-worms crawling slowly about 
upon its surface while it carries them in its diurnal rota- 
tion. As every one knows, the sun in winter is far to 
the south of the equator, and in the summer far to 
the north, apparently completing a yearly circuit of the 
heavens on a path known as the ecliptic. It crosses the 
equator, therefore, twice a year, passing from the south 
side of it to the north about March 21 (this is now 
true, since leap j^ear was skipped in 1900), and alivays 
at the same point, neglecting for the present the effect 
of what is known as "precession." This point, the 
celestial Greenwich, is called the Vernal Equinox, and 
is made the starting-point for many astronomical reckon- 
ings. Unfortunately it is not marked by any conspicuous 
star; but a line drawn from the Pole-star through Beta 
Cassiopeia (the westernmost or " preceding " star in the 
zigzag) (see Map I) and continued 90° from the pole, 
strikes very near it. In Fig. 6, X represents this point. 
It is also called the First of Aries, and designated by the 
symbol °f . 

18. Right Ascension. — The right ascension of a star is 
the arc of the celestial equator intercepted betiveen the vernal 
equinox and the point ivhere the star s hour-circle cuts the 
equator, and is reckoned always eastward from the equinox 
and completely around the circle. It may be expressed 



18 LESSONS IN ASTRONOMY 

either in degrees or in hours. 1 A star one degree west of 
the equinox has a right ascension of 359°, or of 23 h 56 m . 
Evidently the diurnal motion does not affect the right 
ascension of a star, but this, like the declination, remains 
practically unchanged for years. In Fig. 6, if X be the 
vernal equinox, the right ascension of m is the arc XY 
measured from X eastward. 

19. Thus we can define the position of a star either by 
its altitude and azimuth, which tell how high it is in the 
sky, and how it "bears," as a sailor would say; or we 
may use its right ascension and declination, which do not 
change from day to day (not perceptibly at least), and so 
are better adapted to mapping purposes, corresponding as 
they do precisely to latitude and longitude upon the surface 
of the earth. 

Perhaps the easiest way to think of these celestial circles 
is the following: Imagine a tall pole standing straight up 
from the observer, having attached to it at the top (the 
zenith) two half circles coming down to the level of the 
observer's eye, one of them running north and south 
(the meridian), and the other east and west (the prime 
vertical). The bottoms of these two semicircles are con- 
nected by a complete circle (the horizon) at the level of 
the eye. This framework, immense but fortunately only 
imaginary and so not burdensome, the observer takes 
with him wherever he goes, keeping always at its center, 
while over it apparently turns the celestial sphere ; really, 
of course, he and the earth and his framework turn 
together under the celestial sphere. 

1 Twenty-four hours of right ascension or hour-angle = 360° ; one 
hour = 15°. 



INTRODUCTION 19 

The other circles (the celestial equator and the hour- 
circles) are drawn upon the celestial sphere itself and are 
not affected at all by the observer's journeys, but are as 
fixed as the poles and meridians upon the earth ; the stars 
also, to all ordinary observation, are fixed upon the sphere 
just as cities are upon the earth. They really move, of 
course, and swiftly, as has been said before, but they are 
so far away that it takes centuries, as a rule, to produce 
the slightest apparent change of place. 

20. Celestial Latitude and Longitude. — A different way of 
designating the positions of the heavenly bodies in the sky has come 
down to us from very ancient times. Instead of the equator it makes 
use of another circle of reference in the sky, known as the Ecliptic. 
This is simply the apparent path described by the sun in its annual 
motion among the stars; for the sun appears to creep around the 
celestial sphere in a circle once every year, and the Ecliptic may be 
defined as the intersection of the plane of the earth's orbit with the 
celestial sphere, just as the celestial equator is the intersection of the 
earth's equator : the vernal equinox is one of the points where the two 
circles cross. Before the days of clocks, the Ecliptic was in many 
respects a more convenient circle of reference than the equator and 
was almost universally used as such by the old astronomers. Celestial 
longitude and latitude are measured with reference to the Ecliptic, 
in the same way that right ascension and declination are measured 
with respect to the equator, except that celestial longitude cannot be 
expressed in hours, minutes, and seconds of time like right ascen- 
sion. Too much care can hardly be taken to avoid confusion between 
terrestrial latitude and longitude and the celestial quantities that bear 
the same name. 



CHAPTER II 



URANOGRAPHY 



Globes and Star-Maps — Star Magnitudes — Designation of the Stars — The 

Constellations 



Note. — It is hardly necessary to say that this chapter is to be 
treated by the teacher differently from the rest of the book. It is to 
be dealt with, not as recitation matter, but as field-work : to be 
taken up at different times during the course as the constellations 
make their appearance in the evening sky. 

For convenience of reference we add the following alphabetical 
list of the constellations described or mentioned in the chapter : 



Article 

Andromeda 35 

Anser, see Yulpectila ... 69 

Antinoiis, see Aquila . . . 71 

Antlia . 62 

Aquarius 78 

Aquila (not Aquila) . . . 71 

Argo Navis 51 

Aries 38 

Auriga 41 

Bootes 59 

Camelopardus 31 

Cancer 52 

Canes Venatici .... 58 

Can is Major 49 

Canis Minor 48 

Capricornus 73 

Cassiopeia 28 



Article 

Centaur us 62 

Cepheus 29 

Cetus 39 

Columba 45 

Coma Berenices .... 57 

Corona Borealis .... 60 

Corvus 55 

Crater ....... 55 

Cygnus 68 

Delphinus 74 

Draco 30 

Eqmileus ...... 75 

Eridanus 44 

Gemini 47 

Grus 79 

Hercules 66 

Hydra 55 



20 



URAXOCtRAPHY 



21 





Article 


Lacerta . . . 


. ... 76 


Leo .... 


.... 53 


Leo Minor . 


.... 54 


Lepus . . . 


. ... 45 


Libra .... 


. ... 61 


Lupus 


. ... 62 


Lvnx .... 


.... 46 


Lyra .... 


. ... 67 


Monoceros 


.... 50 




.... 64 


Ophiuchus . 


. ... 65 


Orion 




Pegasus . . . 


77 


Perseus . 


.... 40 


Phoenix . 


. ... 39 


Pisces .... 


. ... 36 



Article 

Piscis Australis . . . . 70 

(Pleiades) 42 

Sagitta 70 

Sagittarius 72 

Scorpio 63 

Sculptor 39 

Serpens 65 

Serpentarius, see Ophiuchus 65 

Sextans 54 

Taurus 42 

Taurus Poniatovii . . . 65 

Triangulum 37 

Ursa Major 26 

Ursa Minor 27 

Virgo 56 

Yulpecula 69 



21. Globes and Star-Maps . — In order to study the con- 
stellations conveniently, it is necessary to have either a 
celestial globe or a star-map, by which to identify the 
stars. The globe is better and more accurate, if of suffi- 
cient size, but is costly and rather inconvenient. (For a 
figure and description of the globe, see Appendix, Sec. 400.) 
For most purposes a star-map will answer just as well as 
the globe, but it can never represent any considerable por- 
tion of the sky correctly without more or less distortion of 
all the lines and figures near the margin of the map. Such 
maps are made on various systems, each presenting its own 
advantages. In all of them the heavens are represented 
as seen from the inside, and not as on the globe, which 
represents the sky as if seen from the outside. 

22. Star-Maps of this Book. — We present a series of 
four small maps, which, though hardly on a large enough 



22 LESSONS IN ASTRONOMY 

scale to answer every purpose of a complete celestial atlas, 
are quite sufficient to enable the student to trace out the 
constellations, and to identify the principal stars. In the 
map of the north circumpolar regions (Map I) the pole is 
in the center, and at the circumference are numbered the 
twenty-four hours of right ascension. The parallels of dec- 
lination are represented by equidistant concentric circles. 
On the three other rectangular maps, which show the equa- 
torial belt of the heavens lying between 50° north and 
50° south of the equator, the parallels of declination are 
horizontal lines, while the hour-circles are represented by 
vertical lines, also equidistant, but spaced at a distance 
which is correct, not at the equator but for declination 35°. 
This keeps the distortion within reasonable bounds, even 
near the margin of the map, and makes it very easy to lay 
off the places of any object for which the right ascension 
and declination are given. The ecliptic is the curved line 
which extends across the middle of the map. The top of 
the map is north ; and the east is to the left, instead of 
being at the right hand, as in a map of the earth's sur- 
face ; so that if the observer faces the south, and holds the 
map up before and above him, the constellations which are 
near the meridian will be pretty truly represented. 

The hours of right ascension are indicated on the central hori- 
zontal line, which is the celestial equator, and at the top of the map 
are given the names of the months. The word " September/' for 
instance, means that the stars which are directly under it on the map 
will be near the meridian about 9 o'clock in the evening during that 
month. 

23. Star Magnitudes. — To the eye the principal differ- 
ence in the appearance of the different stars is in their 



URANOGRAPHY 23 

brightness, or their so-called " magnitude." Hipparchus 
(125 B.C.) and Ptolemy divided the visible stars into six 
classes, the brightest fifteen or twenty being called first- 
magnitude stars, and the faintest which can be seen by 
the naked eye being called sixth. 

It has since been fonnd that the light of the average first-magni- 
tude star is just about one hundred times as great as that of the 
sixth ; and at this rate the light of a first-magnitude star should be 
a trifle more than equal to two and a half second-magnitude stars, 
and a second-magnitude star, to two and a half third-magnitude 
stars, etc. 

Our maps show all the stars down to the fifth magnitude 
— about a thousand in number — and all which can be 
seen in a moonlight night. A few smaller stars are also 
inserted where they mark some particular configuration 
or point out some interesting telescopic object. A varia- 
ble star is denoted by var. below the star symbol. A few 
clusters and nebulae are also indicated. The letter M. 
against one of these stands for " Messier," who made the 
first catalogue of 103 such objects in 1784; e.g., M. 51 
designates No. 51 on Messier's list. 

For reference purposes and for study of the heavens in detail, the 
more elaborate star-atlases of Proctor, Heis, Upton, or Schurig are 
recommended, especially the last, which contains a great amount 
of useful information in addition to the maps, and is very cheap 
compared with the others. The student or teacher who possesses a 
telescope will also find an invaluable accessory to it in Webb's 
" Celestial Objects for Common Telescopes." (Published by Long- 
mans, Green &f Co., New York.) 

24. Designation of the Stars. — A few of the brighter 
stars are designated by names of their own, and upon the 



24 LESSONS IN ASTRONOMY 

map those names which are in most common use are indi- 
cated. 1 Generally, however, the designation of visible stars 
is by the letters of the Greek alphabet, on a plan proposed 
in 1603 by Bayer, and ever since followed. The letters 
are ordinarily applied nearly in the order of brightness, 
Alpha being the brightest star in the constellation and 
Beta the next brightest; but they are sometimes applied 
to the stars in their order of position rather than in that 
of brightness. When the stars of a constellation are so 
numerous as to exhaust the letters of the Greek alphabet, 
the Roman letters are next used, — and then, if necessary, 
we employ the numbers which Flamsteed assigned a cen- 
tury later. At present every star visible to the naked eye 
can be referred to and identified by its number or letter in 
the constellation to which it belongs. (For the Greek 
alphabet, see Appendix, page 406.) 

25. We begin our study of Uranography with the con- 
stellations which are circumpolar (i.e., within 40° of the 
north pole), because these are always visible in the United 
States and so can be depended on to furnish land- (or 
rather sky) marks to aid in tracing out the others. Since 
in the latitude of New York the elevation of the pole is 
about 41°, it follows that there (and this is approximately 
true of the rest of the United States) all the constella- 
tions which are within 41° of the north pole will move 
around it once in twenty-four hours without setting. For 
this reason they are called circumpolar. Map I contains 
them all. 

*By far the best book upon the subject of stellar nomenclature is 
Allen's " Star-Names and their Meanings. " It is full of interesting matter 
relating to the constellations and the myths and legends attached to them. 






URAXOGRAPHY 25 

26. Ursa Major, the Great Bear (Map I). — Of these 
circumpolar constellations none is more easily recognized 
than Ursa Major. Assuming the time of observation as 
about 8 o'clock in the evening on September 22, it will be 
found below the pole and to the west. Hold the map so 
that VIII is at the bottom, and it will be rightly placed 
for the time assumed. 

The familiar Dipper is sloping downward in the north- 
west, composed of seven stars, all of about the second mag- 
nitude, excepting Delta (at the junction of the handle to the 
bowl), which is of the third magnitude. The stars Alpha 
(.Dubhe) and Beta (Merak) are known as the " Pointers," 
because a line drawn from Beta through Alpha and pro- 
duced about 30° passes very near the Pole-star. The 
dimensions of the Dipper furnish a convenient scale of 
angular measure. From Alpha to Beta is 5°; from Alpha 
to Delta is 10° ; and from Alpha to Eta, at the extremity 
of the Dipper-handle (which is also the Bear's tail), is 26°. 
The Dipper (known also in England as the u Plough " and 
as the " Wain," or wagon) comprises but a small part of 
the whole constellation. The head of the Bear, indicated 
by a small group of scattered stars, is nearly on the line 
from Delta through Alpha, carried on about 15° ; at the 
time assumed (September 22, 8 o'clock) it is almost exactly 
under the pole. 

Three of the four paws of the creature are marked each 
by a pair of third- or fourth-magnitude stars li° or 2° 
apart. The three pairs are nearly equidistant, about 20° 
apart, and almost on a straight line parallel to the diagonal 
of the Dipper-bowl from Alpha to Gamma, but some 20° 
south of it. At the time assumed they are all three very 



26 LESSONS IN ASTRONOMY 

near the horizon for an observer in latitude 40°, but during 
the spring or summer, when the constellation is high in 
the sky, they can be easily made out. 

The star Zeta (Mizar), at the bend in the handle, is 
easily recognized by the little star Alcor near it. Mizar 
itself is a double star, easily seen as double with a small 
telescope, and one of the most interesting recent astro- 
nomical results is the discovery that it is really triple, the 
larger of the two stars being itself a " spectroscopic double," 
invisibly so to the telescope, but revealing its double char- 
acter by means of the lines in its spectrum. (See Sec. 373.) 
The star Xi, the southern one of the pair, which marks the 
left-hand paw, is also double and binary, i.e., the two stars 
which compose it revolve about their common center of 
gravity in about sixty-one years. (For diagram of the 
orbit, see Fig. 89, Sec. 369.) It was the first binary whose 
orbit was computed. 

According to the ancient legends, Ursa Major is Callisto, the 
daughter of Lycaon, king of Arcadia. The jealousy of Juno 1 
changed her into a bear, and afterwards Jupiter placed her among 
the constellations with Areas her son, who became Ursa Minor. 
One of the quaint old authors explains the very un-bearlike length 
of the creatures' tails by saying that they stretched as Jupiter lifted 
them to the sky. 

27. Ursa Minor, the Lesser Bear (Map I). — The line 
of the Pointers unmistakably marks out the Pole-star 

1 We have followed throughout the Roman nomenclature of the gods 
and heroes, as used by Virgil and Ovid; but the reader should be reminded 
that, in many important respects, these Roman personages differ from 
the Greek divinities who were identified with them. It should be said, 
also, that in many cases the old legends are greatly confused and often 
contradictory ; as, for instance, in the case of Hercules. 



URANOGRAPHY 27 

(Polaris), a star of the second magnitude, standing quite 
alone. It is at the end of the tail of Ursa Minor, or at 
the extremity of the handle of the "Little Dipper"; for 
in Ursa Minor, also, the seven principal stars form a dipper, 
though with the handle bent in a different way from that 
of the other Dipper. Beginning at Polaris, a curved line 
(concave towards Ursa Major) drawn through Delta and 
Epsilon brings us to Zeta, where the handle joins the 
bowl. Two bright stars (second and third magnitude), 
Beta and Gamma, correspond to the Pointers in the large 
Dipper, and are known as the "Guardians of the Pole"; 
Beta is named Kochab, The pole now lies about 1£° from 
the Pole-star, on the line joining it to Mizar (at the bend 
in the handle of the large Dipper). 

It has not always been so. Some 4000 years ago the star Thuban 
(Alpha Draconis) was the Pole-star, and 2000 years ago the present 
Pole-star was very much farther from the pole than now. At present 
the pole is coming nearer to the star, and towards the close of the next 
century it will be within half a degree of it. Twelve thousand years 
hence the bright star Alpha Lyras will be the Pole-star, — and this not 
because the stars change their positions, but because the axis of the 
earth slowly changes its direction, owing to precession. (See Sec. 125.) 

The Greek name of the Pole-star was Cynosura, which 
means the "tail of the Dog," indicating that at one time 
the constellation was understood to represent a Bog instead 
of a Bear. 

As already said (Sec. 26), this constellation is by many writers 
identified with Areas, Callisto's son. But more generally Areas is 
identified with Bootes. 

The Pole-star is double, having a small companion barely 
visible with a telescope of two or three inches diameter. 



28 LESSONS IN ASTRONOMY 

28. Cassiopeia (Map I). — This constellation lies on the 
opposite side of the pole from the Dipper, and at about 
the same distance from it as the Pointers. It is easily 
recognized by the zigzag, " rail-fence " configuration of the 
five or six bright stars that mark it. With the help of 
the rather inconspicuous star Kappa, one can make out of 
them a pretty good chair with the feet turned away from 
the pole. But this is wrong. In the recognized figures 
of the constellation the lady sits with feet towards the 
pole, and the bright star Alpha is in her bosom, while 
Zeta and the other faint stars south of Alpha are in her 
head and uplifted arms ; Iota, on the line from Delta to 
Epsilon produced, is in the foot. The order of the prin- 
cipal stars is easily remembered by the word " Bagdei," 
i.e., Beta, Alpha, Gamma, Delta, Epsilon, Iota. 

Alpha, which is slightly variable in brightness, is known 
as Schedir; Beta is called Caph. The little star Eta, which 
is about half-way between Alpha and Gamma, a little off the 
line, is a very pretty double star, — the larger star orange, 
the smaller one purple. It is binary (i.e., the two stars re- 
volve around each other), with a period of about 206 years. 

In the year 1572 a famous temporary star made its 
appearance in this constellation, at a point on the line 
drawn from Gamma through Kappa, and extended about 
half its length. It was carefully observed and described 
by Tycho Brahe, and at one time was bright enough to be 
seen easily in broad daylight. There has been an entirely 
unfounded notion that this was identical with the star of 
Bethlehem, and there has been an equally unfounded 
impression that its reappearance may be expected about 
the present time. 



URANOGRAPHY 29 

Cassiopeia was the wife of Cepheus, king of Libya, and the mother 
of Andromeda, who was rescued from the sea-monster, Cetus, by Per- 
seus, who came flying through the air, and used the head of Medusa 
(which he still holds in his hand) to turn his adversaries to stone. 
Cassiopeia had indulged in too great boasting of her daughter's 
beauty, and thus excited the jealousy of the Nereids, at whose insti- 
gation the sea-monster was sent by Neptune to ravage the kingdom. 

29. Cepheus (Map I). — This constellation, though large, 
contains very few bright stars. At the assumed time (8 
o'clock, September 22) it is above Cassiopeia and to the 
west, not having quite reached the meridian above the 
pole. A line carried from Alpha Cassiopeia through Beta, 
and produced 20°, will pass very near to Alpha Cephei, a 
star of the third magnitude in the king's right shoulder. 
Beta Cephei is about 8° north of Alpha, and Gamma about 
12° from Beta, both also of the third magnitude. Gamma 
is so placed that it is at the obtuse angle of a rather flat 
isosceles triangle of which Beta Cephei and the Pole-star 
form the other two corners. Cepheus is represented as 
sitting behind Cassiopeia (his wife) with his feet upon 
the tail of the Little Bear, Gamma being in his left knee. 
His head is marked by a little triangle of fourth- magnitude 
stars, of which Delta is a remarkable variable with a period 
of 5 J days. It is worth noting tha,t there are several other 
small variable stars in the same neighborhood (none of them 
bright enough to be shown upon the map). Beta is a very 
pretty double star. 

30. Draco, the Dragon (Map I). — The constellation of 
Draco is characterized by a long, winding line of stars, 
mostly small, extending half-way around the pole and 
separating the two Bears. A line from Delta Cassiopeia 
drawn through Beta Cephei and extended about as far 



30 LESSONS IN ASTRONOMY 

again will fall upon the head of Draco, marked by an 
irregular quadrilateral of stars, two of which are of the 2J 
and 3 magnitude. These two bright stars about 4° apart 
are Beta and Gamma. The latter (named Etanin), in its 
daily revolution, passes almost exactly through the zenith 
of Greenwich, and it was by observations upon it that the 
" aberration of light" was discovered. (See Sec. 435.) 
The nose of Draco is marked by a smaller star, Mu, some 
5° beyond Beta, nearly on the line drawn through it from 
Gamma. From Gamma we trace the neck of Draco, east- 
ward and downward 1 toward the Pole-star, until we come 
to Delta and Epsilon and some smaller stars near them. 

There the direction of the line is reversed, as shown 
upon the map, so that the body of the monster lies between 
its own head and the bowl of the Little Dipper, and winds 
around this bowl until the tip of the tail is reached, at the 
middle of the line between the Pointers and the Pole-star. 
The constellation covers more than twelve hours of right 
ascension. 

One star deserves special notice, the star Alpha, or 
Thuban, a star of 3i magnitude, which lies half-way 
between Zeta Ursse Majoris (Mizar) and Gamma Ursa 
Minoris. Four thousand seven hundred years ago it was 
the Pole-star, and then within a quarter of a degree of 
the pole, much nearer than Polaris is at present or ever 
will be. It is probable also that its brightness has con- 
siderably fallen off within the last 200 years, since among 
the ancient astronomers it was always reckoned as of the 
second magnitude and is not now much above the fourth. 

1 The description applies strictly only at the time assumed, 8 o'clock, 
September 22. 



URANOGRAPHY 31 

The so-called "Pole of the Ecliptic" is in this constella- 
tion, i.e., the point which is 90° distant from every point 
in the Ecliptic, the circle annually described by the sun. 
This point (see map) is the center around which precession 
causes the pole to move nearly in a circle (see Sec. 126) 
once in 25,800 years. 

The mythology of this constellation is doubtful. According to 
some it is the dragon which Cadmus slew, afterwards sow 7 ing its teeth, 
from which sprung up the harvest of armed men w ho fought and slew 
each other, leaving only the five survivors who were the founders of 
Thebes. Others say that it w T as the dragon who watched the golden 
apples of the Hesperides, and was killed by Hercules when he cap- 
tured that prize. This accords best with the fact that in the heavens 
Hercules has his foot on the dragon's head. 

31 . Camelopardus. — This is the only remaining one of the strictly 
circumpolar constellations, — a modern one containing no stars above 
fourth magnitude, and established by Hevelius (1611-1687) simply to 
cover the great empty space between Cassiopeia and Perseus on one 
side, and Ursa Major and Draco on the other. The animal stands 
on the head and shoulders of Auriga, and his head is between the 
Pole-star and the tip of the tail of Draco. 

The two constellations of Perseus (which at the time assumed is 
some 20° below Cassiopeia) and of Auriga are partly circumpolar, 
but on the whole can be more conveniently treated in connection 
with the equatorial maps. Capella, the brightest star of Auriga, 
and next to Yega and Arcturus the brightest star in the northern 
hemisphere, is at the time assumed (8 o'clock, September 22) a few 
degrees above the horizon in the northeast. Between it and the nose 
of Ursa Major lies part of the constellation of the Lynx, a modern 
one, made, like Camelopardus, by Hevelius merely to fill a gap, and 
without any large stars. 

32. The Milky Way in the Circumpolar Region The 

only circumpolar constellations traversed by the Milky 
Way are Cassiopeia and Cepheus. It enters the circumpolar 



32 LESSONS IN ASTRONOMY 

region from the constellation of Cygnus, which at the 
assumed time is near the zenith, sweeps down across 
the head and shoulders of Cepheus, and on through 
Cassiopeia and Perseus to the northeastern horizon in 
Auriga. There is one very bright patch a few degrees 
north of Beta Cassiopeise, and half-way between Delta 
Cassiopeia and Gamma Persei there is another bright 
cloud in which is the famous double cluster of the 
" sword-handle of Perseus," — a beautiful object for even 
the smallest telescope. 

33. For the most part the constellations shown upon 
the circumpolar map (I) will be visible every night in the 
northern part of the United States. At places farther 
south the constellations near the rim of the map will 
stay below the horizon for a short time every twenty- 
four hours, since the height of the pole always equals the 
latitude of the observer, and therefore only those stars 
which have a polar distance less than the latitude will 
remain constantly visible. In other words, if, with the 
pole as a center, we draw a circle with a radius equal to 
the height of the pole above the horizon, all the stars 
within this circle will remain continually above the 
horizon. This is called the circle of " Perpetual Appa- 
rition" (Sec. 85). At New Orleans, in latitude 30°, its 
radius, therefore, is only 30°, and only those stars which 
are within 30° of the pole will make a complete circle 
without setting. At stations in the northern part of the 
United States, as Tacoma, it is nearly as large as the 
whole map. 

34. Before proceeding to consider the other constella- 
tions, the student should be reminded that he will have 



URANOGRAPHY 33 

to select those that are conveniently visible at the time 
of the year when he happens to be studying the subject, 
and that, if he wishes to cover the whole sky, he must take 
up the subject more than once, and at various seasons of the 
year. The constellations near the southern limits of the 
map can be seen only a few weeks in each year. 

He will also be likely to be occasionally perplexed by 
finding in the heavens certain conspicuous stars not on 
the maps, — stars much brighter than any that are given. 
These are the planets Venus, Jupiter, Mars, and Saturn, 
called planets — i.e., " wandering stars " — just because they 
continually change their place, and so cannot be mapped. 
The student will find it interesting and instructive, how- 
ever, to dot down upon the star-map every clear night the 
places of any planets he may notice, and thus to follow 
their motion for a month or two. 

Remember also that on these maps east always lies on 
the left hand, so that the map should be held between 
the eye and the sky in order to represent things cor- 
rectly. We begin with Andromeda at the northwest 
corner of Map II. 

35. Andromeda (Maps II and IV). November.— Andromeda 
will be found exactly overhead in our latitudes about 
9 o'clock in the middle of November. Its characteristic 
configuration is the line of three second-magnitude stars, 
Alpha, Beta, and Gamma, extending east and north from 
Alpha (Alpheratz), which itself forms the northeast corner 
of the so-called " Great Square of Pegasus," and is some- 
times lettered as Delta Pegasi. This star may readily be 
found by extending an imaginary line from Polaris through 
Beta Cassiopeia and producing it about as far again ; Alpha 



34 LESSONS IN ASTRONOMY 

is in the head of Andromeda, Beta (Mirach) in her waist, 
and Gamma (Almaach) in her left foot. A line drawn 
northwesterly from Beta, nearly at right angles to the 
line Beta Gamma, will pass through Mu at a distance of 
about 5°, and produced another 5° will strike the "great 
nebula," which is visible to the naked eye like a little 
cloud of light, and forms a small obtuse-angled triangle 
with Nu and a little sixth-magnitude star. Andromeda 
has her mother, Cassiopeia, close by on the north, with 
her father, Cepheus, not far away, while at her feet is 
Perseus, her deliverer. Her head rests upon the shoulder 
of Pegasus. In the south, beyond the constellations of 
Aries and Pisces, Cetus, the sea-monster, who was to have 
devoured her, stretches his ungainly bulk. 

We have already mentioned the nebula. Another very pretty 
object is Gamma, which in a small instrument is a double star, the 
Larger one orange, the smaller a greenish blue. The small star is 
itself double, making the system really triple, but as such is beyond 
the reach of any but very large instruments. 

When Neptune sent the leviathan, Cetus, to ravage Libya, the 
oracle of Amnion announced that the kingdom could be delivered 
only if Cepheus would give up his daughter. He assented and 
chained the poor girl to a rock to await her destruction. But Per- 
seus, returning through the air from the slaying of the Gorgon, 
Medusa, saw her, rescued her, won her love, and made her his wife. 

36. Pisces, the Fishes (Map II). November. — Imme- 
diately soutli of Andromeda lies Pisces, the first of the con- 
stellations of the Zodiac, 1 which is a belt 16° wide (8° on 

1 The word is derived from the Greek word zobn ( a living creature) 
and indicates that all the constellations in it (Libra alone excepted) are 
animals. The zodiacal constellations are for the most part of remote 
antiquity, antedating by many centuries even the Greek mythology. 



URANOGRAPHY 35 

each side of the ecliptic), encircling the heavens, and 
including the space within the limits of which the sun, the 
moon, and all the principal planets perform their apparent 
motions. At present, in consequence of precession, it 
occupies the sign of Aries. (See Sec. 126.) It has not a 
single conspicuous star, and is notable only as now con- 
taining the Vernal Equinox, or First of Aries, which lies 
near the southern boundary of the constellation in a pecul- 
iarly starless region. A line from Alpha Andromedae 
through Gamma Pegasi, continued as far again, strikes 
about 2° east of the point. The body of one of the two 
fishes lies about 15° south of the middle of the southern 
side of the " Great Square of Pegasus," and is marked by 
an irregular polygon of small stars, 5° or 6° in diameter. 
A long crooked " ribbon" of little stars runs eastward 
for more than 30°, terminating in Alpha Piscium (called 
El Rischa, or " the knot "), a star of the fourth magni- 
tude 20° south of the head of Aries. From there another 
line of stars leads up northwest in the direction of Delta 
Andromedse to the northern fish, which lies in the vacant 
space south of Beta Andromedse. 

Alpha is a very pretty double star, the two components being 
about 2" apart. 

The mythology of this constellation is not very well settled. One 
story is that the fishes are Venus and her son Cupid, who were thus 
transformed when endeavoring to escape from the giant Typhon. 
The northern fish is Cupid, the southern his mother. 

37. Triangulum, or Deltoton, the Triangle (Map II). 
December. — This little constellation, insignificant as it 
is, is one of Ptolemy's ancient forty-eight. It lies half-way 
between Gamma Andromedse and the head of Aries, and 



36 LESSONS IN ASTRONOMY 

is characterized by three stars of the third and fourth mag- 
nitude, easily made out by the help of the map. 

It may be regarded as a canonization of " Divine Geometry," but 
has no special mythological legend connected with it. 

38. Aries, the Ram (Map II). December. — This is 
the second of the zodiacal constellations, now occupying 
the sign of Taurus. It lies just south of Triangulum and 
Perseus. Its characteristic star-group is that composed of 
Alpha (Hamal), Beta, and Gamma (see map), about 20° due 
south of Gamma Andromedse. Alpha, a star of 2£ mag- 
nitude, is fairly conspicuous, forming a large isosceles tri- 
angle with Beta and Gamma Andromedse. 

Gamma Arietis is a very pretty double star with the components 
about 9" apart. It is probably the first double star discovered, 
having been noticed by Hooke in 1664. 

The star 41 Arietis (3^ magnitude), which forms a nearly equilat- 
eral triangle with Alpha Arietis and Gamma Trianguli, constitutes, 
with two or three other stars near it, the constellation of Musca 
(Borealis), a constellation, however, not now generally recognized. 

According to the Greeks, Aries is the ram which bore the Golden 
Fleece and dropped Helle into the Hellespont, when she and her 
brother, Phrixus, were fleeing on its back to Colchis. Long after- 
wards the Argonautic Expedition, with Jason as its head and Her- 
cules as one of its members, sailed from Greece to Colchis to recover 
the fleece, and finally succeeded after long endeavors. 

39. Cetus, the Sea-Monster (Map II). November to 
December. — South of Aries and Pisces lies the huge con- 
stellation of Cetus, the sea-monster, which backs up into 
the sky from the southeastern horizon. The head lies 
some 20° southeast of Alpha Arietis, and is marked by an 
irregular five-sided figure of stars, each side being some 



i 



UR APOGRAPH Y 37 

5° or 6° long. The southern edge of this pentagon is 
formed by the stars Alpha, or Menkar (2 J magnitude), and 
Gamma (3i magnitude) ; Delta lies southwest of Gamma. 
Beta [Deneb Ceti), 1 the brightest star of the constellation 
(2 magnitude), stands by itself nearly 40° west and south 
of Alpha. Gamma is a very pretty double star, but rather 
close for a small telescope, the components being only 
2".5 apart, yellow and blue. 

Cetus is the leviathan that was sent by Neptune to ravage Libya 
and devour Andromeda. Perseus turned him into stone by showing 
him the head of the Gorgon, Medusa. On the globes he is usually 
represented as a nondescript sort of beast, with a face like a puppy's, 
and a tightly curled tail ; as if the Gorgon's head had frightened 
out all his savageness. 

South of Cetus lies the modern constellation of Sculptoris Appa- 
ratus (usually known simply as Sculptor), which, however, contains 
nothing that requires notice here. South of Sculptor, and close to 
the horizon, even when on the meridian, is Phoenix, It has some 
bright stars, but none easily observable in the United States. 

40. Perseus (Maps I and II). January. — Returning 
now to the northern limit of the map, we come to the con- 
stellation of Perseus. Its principal star is Alpha (Algenib), 
rather brighter than the standard second magnitude, and 
situated very nearly on the prolongation of the line of the 
three chief stars of Andromeda. A very characteristic 
configuration is the so-called " segment of Perseus " 
(Map I), a curved line formed by Delta, Alpha, Gamma, 
and Eta, with some smaller stars, concave towards the 
northeast, and running along the line of the Milky Way 
towards Cassiopeia. The remarkable variable star, Beta, 
or Algol, is situated about 9° south and a little west of 

1 Deneb signifies " tail," and there are several stars of that name. 



38 LESSONS IN ASTRONOMY 

Alpha, at the right angle o( a right-angled triangle which 
it forms with Alpha, Persei and Gamma Andromedae. 
Algol and a few small stars near it form "Medusa's 
Head," which Perseus carries in his hand. (For further 
particulars and recent discoveries regarding this star, see 
Sees. 358 and 860.) 

In this constellation, nearly in the center of the triangle 
formed by Algenib with Algol and Bpsilon, appeared the 
remarkable temporary star, or Nbva^ of 1901, the most 
brilliant of its kind for nearly 300 years, (See Sec, 355*.) 

Epsilon is a very pretty double star w i 1 1 1 the components about 
so" apart ; but the most beautiful telescopic object in the constel- 
lation, perhaps the finest indeed in the whole heavens for a small 
telescope, is the pair of clusters about half-way between Gamma 
Persei and Delta Cassiopeise, visible to the naked eye as a bright 
knot in the Milky Way, and already referred to in Sec. 32. 

Perseus was the son of Danae' by Jupiter, who won her in a 
shower of gold. He was sent by his enemies on the desperate 
venture of capturing the head of Medusa, the only mortal one of 
the three Gorgons, which were frightful female monsters with wings, 
tremendous claws, and brazen teeth, and serpents for hair; of such 
aspect that the sight turned to stone all who looked at them. The 
gods helped Perseus by various gifts, which enabled him to approach 

his victim, invisible and unsuspected, and to deal the fata] blow- 
without Looking at the sight himself. From the Mood o( Medusa, 
where her body fell, sprang Pegasus, the winged horse, and where 
the drops fell on the sands of Libya, as Perseus was flying across 
the desert, thousands of venomous serpents swarmed. On his way. 
returning home, he saw and rescued Andromeda, as already men- 
tioned (Sees. 28 and 85), Hercules was one of their descendants. 

41. Auriga, the Charioteer ^Maps I and II). January. — 
Proceeding east from Perseus we come to Auriga, who is 
represented as holding in his arms a goat and her kids. 






URANOGRAPHY 39 

The constellation is instantly recognized by the bright 
yellow star Capella (the Goat) and her attendant "Hcedi " 
(the Kids). Alpha Aurigse {Capella) is, according to 
Pickering, precisely of the same brightness as Vega, both 
of them being about J of a magnitude fainter than Arc- 
turus, but distinctly brighter than any other stars visible 
in our latitudes except Sirius itself. The spectroscope 
shows that Capella is very similar in character to our own 
sun, though probably vastly larger. It has recently been 
discovered to be a spectroscopic binary like Mizar (Sec. 26). 
About 10° east of Capella is Beta Aurigae (Menkalinan) 
of the second magnitude ; Epsilon, Zeta, and Eta, which 
form a long triangle 4° or 5° south of Alpha, are the Kids. 

There seems to be no well-settled mythological history for this con- 
stellation, though some say that he is the charioteer of (Enomaus, 
king of Elis; while others connect him with the story of Phaethon, 
the son of Apollo, who borrowed the horses of his father and was 
overthrown in mid-heaven. The goat is supposed to be Amalthea. 
the goat which suckled Jupiter in his infancy. Capella and the 
Kids were always regarded by astrologers as of kindly influence, 
especially towards sailors. 

42. Taurus, the Bull (Map II). January. — This, the 
third of the zodiacal constellations, lies directly south of 
Perseus and Auriga, and north of Orion. It is unmistak- 
ably characterized by the Pleiades, and by the V-shaped 
group of the Hyades which forms the face of the bull, 
with the red Aldebaran (Alpha Tauri), a standard first- 
magnitudc star, blazing in the creature's eye. as he charges 
down upon Orion. His long horns reach out towards 
Gemini and Auriga, and are tipped with the second- and 
third-magnitude stars, Beta and Zeta. As in the case of 



40 LESSONS IN ASTRONOMY 

Pegasus, only the head and shoulders appear in the con- 
stellation. Six of the Pleiades are easily visible, and on 
a dark night a fairly good eye will count nine of them. 
With a three-inch telescope about one hundred stars are 
visible in the cluster, which is more fully described with a 
figure in Sec. 376. The brightest of the Pleiades is called 
Alcyone, and was assigned to the dignity of the " Central 
Sun" by Maedler (Sec. 386). 

About 1° west and a little north of Zeta is a nebula (Messier 1), 
which has many times been discovered by tyros with a small tele- 
scope as a new comet ; it is an excellent imitation of the real thing. 

According to the Greek legends, Taurus is the milk-w T hite bull 
into which Jupiter changed himself when he carried away Europa 
from Phoenicia to the island of Crete, where she became the mother 
of Minos and the grandmother of Deucalion, the Noah of Greek 
mythology. But Taurus, like most of the other zodiacal constel- 
lations, is really far older than the Greek mythology, and appears 
in the most ancient zodiacs of Egypt, where it w 7 as probably con- 
nected w ith the worship of the bull, Apis ; so also in the ancient 
Astronomy of Chaldea and India. 

The Pleiades were daughters of the giant Atlas. Of the seven 
sisters, one, who married a mortal, lost her brightness, according to 
the legend, so that only six remain visible. Some say that Merope 
was the one who thus gave up her immortality for love, but her star 
is still visible, while Celseno and Asterope are both faint. The now 
recognized names of the stars in the group (see map, Sec. 376) 
include Atlas and Pleione, the parents of the family, as well as the 
seven sisters. As for the Hyades, who were half-sisters of the 
Pleiades, there is less legendary interest in their case. They are 
always called by the poets the "rainy Hyades." 

43. Orion (not O'rion) (Map II). February. — This is 
the most splendid constellation in the heavens. As the 
giant stands facing the bull, his shoulders are marked by 



URANOGRAPHY 41 

the two bright stars Alpha (Betelgeuze, pronounced Betel- 
jeuze) and Gamma (Bellatrix), the former of which in color 
closely matches Aldebaran, though its brightness is some- 
what variable. In his hand he holds up the lion skin, 
indicated by the curved line of little stars between Gamma 
and the Hyades. The top of the club, which he brandishes, 
lies between Zeta Tauri and Mu and Eta Geminorum. His 
head is marked by a little triangle of stars of which Lambda 
is the chief. His belt, through the northern end of which 
passes the celestial equator, consists of three stars of the 
second magnitude, pointing obliquely southeast toward 
Sirius. It is very nearly 3° in length, and is known in Eng- 
land as the " Ell and Yard." From the belt hangs the sword, 
composed of three smaller stars lying more nearly north and 
south; the middle one of them is the multiple, Theta, in the 
great nebula, which even in a small telescope is a beautiful 
object, the finest nebula in the sky. (See Fig. 94, Sec. 378.) 
Beta Orionis, or Rigel, a magnificent white star, is in one of 
his feet, and Kappa is in the knee of the other leg. (Orion 
has only one foot, or if he has another it is hidden behind 
Lepus.) The quadrilateral Alpha, Gamma, Beta, Kappa, 
with the diagonal belt, Delta, Eta, Zeta, once learned can 
never be mistaken for anything else in the heavens. 

Bigel is a very pretty double star, the larger star having a very 
small companion about 10" distant. The two stars at the extremities 
of the belt are also double. 

Orion was a giant and mighty hunter, son of Neptune, and beloved 
by both Aurora and Diana. The legends of his life and exploits are 
numerous, and often contradictory. He conquered every creature 
except the Scorpion, which stung and killed him. As a winter con- 
stellation his influence was counted stormy, and he was greatly 
dreaded by sailors. 



42 LESSONS m ASTRONOMY 

44. Eridanus, the River Po (Map II). January. — This constel- 
lation lies south of Taurus, in the space between Cetus and Orion, 
and extends far below the southern horizon. The portion near the 
south pole has a pair of bright stars, which, of course, are never visible 
at the United States. Starting with Beta (Cursa, as it is called), 
of the third magnitude, about 3° north and a little west of Bigel, one 
can follow a sinuous line of stars westward to the paws of Cetus, 
where the stream turns at right angles and runs southward and 
southwest to the horizon. To trace it conveniently, however, requires 
a map on a larger scale than the one we present. 

45. Lepus and Columba (Map II). February. — The con- 
stellation of Lepus (the Hare), one of Orion's victims, is one 
of the ancient forty-eight, and lies just south of the giant, 
occupying a space of some 15° square. Its characteristic 
configuration is a quadrilateral of third- and fourth-magni- 
tude stars, with sides from 3° to 5° long, about 10° south 
of Kappa Orionis, and 15° west of Sirius. 

Columba, the Dove, lies next south of Lepus, too far 
south to be well seen in the Northern States. Its principal 
star, Alpha (Phact), is of 2i magnitude, and is readily found 
by drawing a line from Procyon to Sirius and prolonging 
it about the same distance. In passing, we may note that 
a similar line drawn from Alpha Orionis through Sirius, 
and produced, will strike near Zeta Argus, or Naos, a star 
about as bright as Phact, — the two lines which intersect 
at Sirius making the so-called " Egyptian X." 

Colnmba is a modern constellation, commemorating Noah's dove 
returning to the ark with the olive branch. 

46. Lynx (Maps I, II, and III). February. — Returning now 
to the northern limit of the map, we find the modern constellation 
of the Lynx lying just east of Auriga, and enveloping it on the north 
and in the circunipolar region, as shown on the map. It contains 



URANOGRAPHY 43 

no stars above the fourth magnitude, and is of no importance except 
as occupying an otherwise vacant space. 

47. Gemini, the Twins (Map II). February and March. 

— This is the fourth of the zodiacal constellations, now 
lying mostly in the sign of Cancer. It contains the sum- 
mer solstitial point — the point where the sun turns from 
its northern motion to its southern in the summer. At 
present it is about 2° west and a little north of the star 
Eta. Gemini lies northeast of Orion and southeast of 
Auriga, and is sufficiently characterized by the two stars 
Alpha and Beta (about 4i° apart), which mark the heads 
of the twins. The southern one, Beta, or Pollux, is now 
the brighter ; but Alpha ( Castor) is much more interesting, 
as being double (easily seen with a small telescope). The 
feet are marked by the third-magnitude stars Gamma and 
Mu, some 10° east of Zeta Tauri. 

Castor and Pollux were the sons of Jupiter by Leda, and ancient 
mythology, especially that of Rome, is full of legends relating to 
them. Many of our readers will remember Macaulay's ballad of " The 
Battle of Lake Regillus," when they won the fight for Rome. They 
were regarded as the special patrons of the sailor, who relied much on 
their protection against the evil powers of Orion and the Hyades. 

48. Canis Minor, the Little Dog (Map III). March. — 

This constellation, about 20° south of Castor and Pollux, 
is marked by the bright star Procyon, which means " before 
the dog," because it rises about half an hour before the 
Dog Star (Sirius). Alpha, Beta, and Gamma form together 
a configuration closely resembling that formed by Alpha, 
Beta, and Gamma Arietis. Procyon, Alpha Orionis, and 
Sirius form a nearly equilateral triangle, with sides of 
about 25°. 



44 LESSONS m ASTRONOMY 

The animal is supposed to have been one of Orion's dogs, though 
some say the dog of Icarus, whom they identify with Bootes. 

49. Canis Major, the Great Dog (Map II). February. — 

This glorious constellation hardly needs description. Its 
Alpha is the Dog Star (Sirius), beyond all comparison the 
brightest star in the heavens, and one of our nearer neigh- 
bors, — so distant, however, that it requires more than 
eight years for light to come to us from it. It is nearly 
pointed at by a line drawn through the three stars at 
Orion's belt. Beta, at the extremity of the uplifted paw, 
is of the second magnitude, and so are several of the stars 
farther south in the rump and tail of the animal, who sits 
up watching his master Orion, but with an eye out for 
Lepus. 

50. Monoceros, the Unicorn (Map II). March. — This is one of 
the modern constellations organized by Hevelius to fill the gap 
between Gemini and Canis Minor on the north, and Argo Navis and 
Canis Major on the south. It lies just east of Orion and has no 
conspicuous stars, but is traversed by a brilliant portion of the Milky 
Way. The Alpha of the constellation (fourth magnitude) lies about 
half-way between Alpha Orionis and Sirius, a little west of the line 
that joins them. 11, or Alpha, Monocerotis, a fine triple star (see 
Fig. 88, Sec. 366), fourth magnitude, is very nearly pointed at by a 
line drawn from Zeta Canis Majoris northward through Beta, and 
continued as far again. 

51. Argo Navis, the Ship Argo (genitive Argus) (Maps II 
and III). March. — This is one of the largest, oldest, and 
most important of the constellations, lying south and east 
of Canis Major. Its brightest star, Alpha Argus (Canopus), 
ranks next to Sirius and is visible in the Southern States, 
but not in the Northern. The constellation, huge as it is, 
is only a half one, like Pegasus and Taurus, — only the 



URANOGRAPHY 45 

stern of a vessel, with mast, sail, and oars ; the stem being 
wanting. In the part of the constellation covered by our 
maps there are no very conspicuous stars, though there are 
some of third and fourth magnitude which lie east and 
southeast of the rump and tail of Canis Major. We have 
already mentioned Zeta, or Naos, at the southeast extremity 
of the "Egyptian X." 

The constellation is so large that for convenience it has recently 
been divided into four sub-constellations, Mains (the mast), Vela 
(the sails), Puppis (the stern), and Carina (the keel or hull). This 
new division sometimes leads to misunderstanding; thus Eta Carinas 
is not always at first recognized as the Eta Argus of older astronomers. 

According to the Greek legends, this is the miraculous ship in 
which Jason and his fifty companions sailed from Greece to Colchis 
to recover the Golden Fleece. It had in its bow a piece of oak from 
the sacred grove of Dodona, which enabled the ship to talk with its 
commander and give him advice. 

Some see in the constellation the ark of Noah. 

52. Cancer, the Crab (Maps II and III). March. — This 
is the fifth of the zodiacal constellations, lying just east of 
Canis Minor. It does not contain a single conspicuous 
star, but is easily recognizable from its position, and in a 
dark night by the nebulous cloud known as Prcesepe, or the 
" Manger," with the two stars Gamma and Delta near it, 
— the so-called Aselli, or " Donkeys." Prasepe, some- 
times also called the " Beehive," is really a coarse cluster of 
seventh- and eighth-magnitude stars, resolvable by an opera- 
glass. The line from Castor through Pollux, produced 
about 12°, passes near enough to it to serve as a pointer. 

The star Zeta is a very pretty triple star, though with a small tel- 
escope it can be seen only as double. It is easily found by a line 
from Castor through Pollux, produced 2± times as far. 



46 LESSONS IN ASTRONOMY 

By the Greeks this was identified as the Crab who attacked 
Hercules when he was fighting the Lernaean Hydra. In the old 
Egyptian zodiacs the Crab is replaced by the Scarabams, or Beetle; 
and in sonic of the more recent zodiacs by a pair of asses, still 
recognized in the name Aselli, given to the two stars Gam ma 
and Delta. 

53. Leo, the Lion (Map III). April East of Cancer 

lies the noble constellation of Leo, which adorns the even- 
ing sky in March and April ; it is the sixth of the zodiacal 
constellations, now occupying the sign of Virgo. Its lead- 
ing star, Regulus, or "Cor Leonis," is of the first magni- 
tude, and two others, Beta (Denebola) and Gamma, are of 
the second magnitude. Alpha, Gamma, Delta, and Beta 
form a conspicuous irregular quadrilateral (see map), the 
line from Regulus to Denebola being about 26° long. 
Another characteristic configuration is the " Sickle," of 
which Regulus is the handle, and the curved line Eta, 
Gamma, Zeta, Mu, and Epsilon is the blade, the cutting 
edge being turned towards Cancer. 

The "radiant" of the November meteors lies between Zeta and 
Epsilon. Gamma, in the Sickle, and at the southeast corner of the 
quadrilateral, is a very pretty double star — binary — with a period 
of about 400 years. 

According bo classic writers, this is the Nemsean Lion which was 
killed by Hercules, as the first of his Twelve Labors; but, like Aries 
and Taurus, the constellation is Ear older bhan the Greeks and stands 
in its present form on all bhe ancient zodiacs. 

54. Leo Minor and Sextans (Map III). April. — Leo Minor 

(the Smaller Lion) is an insignificant modern constellation com- 
posed of a few small stars north of Leo, between it and bhe i'eet 
of Ursa Major. It contains nothing deserving special notice. The 

same remark holds good as bO Sextans (the Sextant\ and even more 
eniphat ieally. 



URANOGRAPHY 47 

55. Hydra (Map III). March to June. — This constel- 
lation, with its riders, Crater (the Cup) and Corvus (the 
Raven), is a large and important one, though not very 
brilliant. The head is marked by a group of five or six 
fourth- and fifth-magnitude stars just 15° south of Prsesepe. 
A curving line of small stars leads down southeast to 
Alpha, Cor Hydrce, or Alphard (which means "the soli- 
tary "), a 2i-magnitude star standing very much alone. 
From there, as the map shows, an irregular line of fourth- 
magnitude stars running far south and then east, almost 
to the boundary of Scorpio, marks the creature's body and 
tail, the whole extending very nearly 90°. About the 
middle of the length of Hydra, and just below the hind 
feet of Leo (30° due south from Denebola), we find the 
little constellation of Crater; and just east of it the still 
smaller but much more conspicuous one of Corvus, with 
two second-magnitude stars in it, and four of the third 
and fourth magnitudes. It is well marked by a character- 
istic quadrilateral (see map), with Delta and Eta together 
at its northeast corner. The order of the letters in Corvus 
differs widely from that of brightness, suggesting that 
changes may have occurred since the letters were applied. 

Epsilon Hydrse and Delta Corvi are pretty double stars, the latter 
easily seen with a small telescope ; colors, yellow and purple. 

Hydra, according to the Greeks, is the immense hundred-headed 
monster which inhabited the Lerngean Marsh, and was killed by Her- 
cules as his second labor. But the Hydra of the heavens has only 
one head, and is probably much older than the legends of Hercules. 

An old legend says that Corvus is Coronis, a nymph who was 
transformed into a raven to escape the pursuit of Neptune. Another 
story is that she was changed into a crow for telling tales of some 
imprudent actions of Jupiter which came under her notice. 



48 LESSONS IN ASTRONOMY 

56. Virgo (Map III). May. — East and south of Leo 
lies Virgo, the seventh zodiacal constellation, mostly in 
the sign of Libra. Its Alpha (Spica Virginis) is of the 
li magnitude and, standing rather alone, 10° south of 
the celestial equator, is easily recognized as the southern 
apex of a nearly equilateral triangle which it forms with 
Denebola (Beta Leonis) to the northwest, and Arcturus 
northeast of it. Beta Virginis, of the third magnitude, is 
14° south of Denebola. A line drawn eastward and a little 
south from Beta (third magnitude) and then carried on, 
curving northward, passes successively (see map) through 
Eta, Gamma, Delta, and Epsilon, of the third magnitude. 
(Notice the word " Begde," like " Bagdei " in Cassiopeia, 
Sec. 28.) 

Gamma is a remarkable binary star, at present easily visible as 
double in a small telescope. Its period is 185 years, and it has 
completed pretty nearly a full revolution since its first discovery. 
(For a diagram of its orbit, see Fig. 89, Sec. 369.) A few degrees 
north of Gamma lies the remarkable nebulous region of Virgo, con- 
taining hundreds of these curious objects ; but for the most part 
they are very faint, and observable only with large telescopes. 

The classic poets recognize Virgo as Astrsea, the goddess of jus- 
tice, who, last of all the old divinities, left the earth at the close of 
the Golden Age. She holds the Scales of Justice (Libra) in one hand, 
and in the other a sheaf of wheat. 

Some identify her with Erigone, the daughter of Icarus or Bootes. 
Others recognize in her the Egyptian Isis. 

57. Coma Berenices, Berenice's Hair (Map III). May. — This 
little constellation, composed of a great number of fifth- and sixth- 
magnitude stars, lies 30° north of Gamma and Eta Virginis, and about 
15° northeast of Denebola. It contains a number of interesting 
double stars, but they are not easily found without the help of a 
telescope equatorially mounted. 






URANOGRAPHY 49 

The constellation was established by the Alexandrian astronomer 
Conon, in honor of the queen of Ptolemy Soter. She dedicated her 
splendid hair to the gods, to secure her husband's safety in war. 

58. Canes Venatici, the Hunting-Dogs (Map III) . May. — 
These are the dogs with which Bootes, the huntsman, is 
pursuing the Great Bear around the pole ; the northern of 
the two is Asterion, the southern Chara. Most of the stars 
are small, but Alpha is of the 2^- magnitude, and is easily 
found by drawing from Eta Ursae Majoris (the star in the 
end of the Dipper-handle) a line to the southwest, perpen- 
dicular to the line from Eta to Zeta (Mizar), and about 
15° long; in England it is generally known as Cor Caroli 
(the Heart of Charles), in allusion to Charles I. With 
Arcturus and Denebola it forms a triangle much like that 
which they form with Spica. 

The remarkable whirlpool nebula of Lord Rosse is situated in this 
constellation, about 3° west and somewhat south of the star Eta 
Ursae Majoris. In a small telescope it is by no means conspicuous, 
but in a large telescope is a wonderful object. 

The constellation is modern, formed by Hevelius. 

59. Bootes, the Huntsman (Maps I and III). June. — 

This fine constellation extends more than 60° in declina- 
tion, from near the equator quite to Draco, where the 
uplifted hand holding the leash of the hunting-dogs over- 
laps the tail of the Bear. Its principal star, Alpha (Arctu- 
rus, meaning " bear- driver " ), is of a ruddy hue, and in 
brightness is excelled only by Sirius among the stars visible 
in our latitudes. It is at once recognizable by its forming 
with Spica and Denebola the great triangle already men- 
tioned (Sec. 56). Six degrees west and a little south of it 
is Eta, of the third magnitude, which forms with it, in 



50 LESSONS IN ASTRONOMY 

connection with Upsilon, a configuration like that in the 
head of Aries. Epsilon is about 10° northeast of Arcturus, 
and in the same direction about 10° farther lies Delta. The 
map shows the pentagon which is formed by these two stars 
along with Beta, Gamma, and Rho. 

Epsilon is a fine double star ; colors, orange and greenish blue ; 
distance, about 3". 

The legendary history of this constellation is very confused. One 
legend makes it to be Icarus, the father of Erigone (Virgo), but the 
one most usually accepted makes it to be Areas, son of Callisto. After 
she was changed to a bear (Ursa Major), her son, not recognizing 
her, hunted her with his dogs, and was on the point of killing her, 
when Jupiter interfered and took them both to the stars. 

60. Corona Borealis, the Northern Crown (Map III). 
June. — This beautiful little constellation lies 20° north- 
east of Arcturus, and is at once recognizable as an almost 
perfect semicircle composed of half a dozen stars, among 
which the brightest, Alpha (Gremrna, or Alphacca), is of the 
second magnitude. The extreme northern one is Theta; 
next comes Beta, and the rest follow on the Bagdei order, 
just as in Cassiopeia. About a degree north of Delta, now 
visible with an opera-glass, is a small star which in 1866 
suddenly blazed out until it became brighter than Alphacca 
itself. (See Sec. 355.) 

The little star Eta is a rapid binary with a period of less than 
forty-two years. At times it can be easily divided by a small 
telescope. 

The constellation is said to be the crown that Bacchus gave to 
Ariadne, before he deserted her on the island of Naxos. 

61. Libra, the Balance (Map III). June. — This is the 
eighth of the zodiacal constellations, lying east of Virgo, 



URANOGRAPHY 51 

bounded on the south by Centaurus and Lupus, on the 
east by the upstretched claw of Scorpio, and on the north 
by Serpens and Virgo. It is inconspicuous, the most 
characteristic figure being the trapezoid formed by the 
lines joining the stars Alpha, Iota, Gamma, and Beta. 
Beta, which is the northern one, is about 30° due east 
from Spica, while Alpha is about 10° southwest of Beta. 
The remarkable variable, Delta Librae, is 4° west and a 
little north from Beta. Most of the time it is of the 4 J or 
5 magnitude, but runs down nearly two magnitudes, to 
invisibility, once in 2 i days ("Algol" type, Sec. 358). 

Libra is the Balance of Virgo, the goddess of justice, and was not 
recognized by the classic writers as a separate constellation until the 
time of Julius Caesar, the space now occupied by Libra being then 
covered by the extended claws of Scorpio. 

The cluster M. 5, situated on the extreme northern border of 
the constellation, is remarkable for the number of variable stars it 
contains (Sec. 361). 

62. Antlia, Centaurus, and Lupus (Map III). April to 
June. — These constellations lie south of Hydra and Libra. 

Antlia Pneumatica (the Air-Pump) is a modern constellation of no 
importance and hardly recognizable by the eye, having only a single 
star as bright as the \\ magnitude. 

Centaurus, on the other hand, is an ancient and exten- 
sive asterism, containing in its south (circumpolar) regions, 
not visible in the United States, two stars of the first mag- 
nitude, Alpha and Beta. Alpha Centauri stands next after 
Sirius and Canopus in brightness and, as far as present 
knowledge indicates, is our nearest neighbor among the stars. 
The part of the constellation which becomes visible in our 



52 



LESSONS IN ASTRONOMY 



latitudes is not especially brilliant, though it contains sev- 
eral stars of the 2i and 3 magnitudes in the region lying 
south of Corvus and Spica Virginis. 

Lupus (the Wolf), also one of Ptolemy's constellations, lies due east 
of Centaurus and just south of Libra. It contains a considerable 
number of third- and fourth-magnitude stars; but it is too low for 
any satisfactory study in our latitudes. It is best seen late in June. 
These constellations contain numerous objects interesting for a 
southern observer, but not observable by us. 

The Centaurs were a fabulous race, half man, half horse, who 
lived in Thessaly and herded cattle. Chiron was the most distin- 
guished of them, the teacher of almost all the Greek heroes in every 
manly and noble art, and the friend of Hercules, by whom, however, 
he was accidentally killed. Jupiter transferred him to the stars. 
(See Sagittarius, Sec. 72.) The wolf is represented as transfixed by 
the Centaur's spear. 

63. Scorpio (or Scorpius; genitive Scorpii), the Scorpion 
(Map IV). July. — This, the ninth of the zodiacal con- 
stellations and the most brilliant of them all, lies southeast 
of Libra, which in ancient times used to form its claws 
(Chelae). It is recognized at once by the peculiar configu- 
ration of the stars, which resembles a boy's kite, with a 
long streaming tail extending far down to the south and 
east, and containing several pairs of stars. The principal 
star of the constellation, Antares, is of the first magnitude, 
and fiery red like the planet Mars. From this it gets its 
name, which means "the rival of Ares" (Mars). Antares 
is a very pretty double star, with a beautiful little green 
companion just to the west of it, not very easy to be seen, 
however, with a small telescope. Beta (second magnitude) 
is in the arch of the kite bow, about 8° or 9° northwest of 
Antares, while the star which Bayer lettered as Gamma 



URANOGRAPHY 53 

Scorpii is well within Libra, 20° west of An tares. (There 
is considerable confusion among uranographers as to the 
boundary between the two constellations.) The other 
principal stars of the constellation are easily found on 
the map. 

Many of them are of the second magnitude. One of the finest 
clusters known, and easily seen with a small telescope, is M. 80, 
which lies about half-way between Alpha and Beta. 

Mu 1 is one of the most remarkable of the spectroscopic binaries 
(Sec. 374), the relative velocity of the two stems of the pair being 
about 300 miles a secondhand the period of revolution only a day 
and ten hours. 

According to the Greek mythology, this is the scorpion that killed 
Orion. It was the sight of this monster of the heavens that fright- 
ened the horses of the sun, when poor Phaethon tried to drive them 
and was thrown out of his chariot. Among astrologers, the influence 
of Scorpio has always been held as baleful to the last degree. 

64. Norma Nilotica, the rule with which the height of the Nile 
was measured, lies west of Scorpio, while Ara lies due south of Eta 
and Theta. Both are modern constellations, small and of no impor- 
tance in our latitudes. 

65. Ophiuchus and Serpens (Map IV). July. — Ophiu- 
chus means the " serpent-holder," and probably refers to 
the great physician JEsculapius. The hero is represented 
as standing with his feet on Scorpio and grasping the 
serpent. The two constellations, therefore, are best treated 
together. The head of Serpens is marked by a group 
of small stars lying just south of Corona and 20° due 
east of Arcturus. Beta and Gamma are the two brightest 
stars in the group, their magnitudes 3i and 4. Delta 
lies 6° southwest of Beta, and there the serpent's body 
bends southeast through Alpha and Epsilon Serpentis 



54 LESSONS m ASTEONOMY 

(see map) to Delta and Epsilon Ophiuchi in the giant's 
hand. The line of these five stars carried upwards passes 
nearly through Epsilon Bootis, and downwards through 
Zeta Ophiuchi. A line crossing this at right angles, nearly 
midway between Epsilon Serpentis and Delta Ophiuchi, 
passes through Mu Serpentis on the southwest and Lambda 
Ophiuchi to the northeast. The lozenge-shaped figure 
formed by the lines drawn from Alpha Serpentis and Zeta 
Ophiuchi to the two stars last mentioned is one of the most 
characteristic configurations of the summer sky. Alpha 
Ophiuchi (2J magnitude) (Ras Alaghue) is easily recog- 
nizable in connection with Alpha Herculis, since they 
stand rather isolated, about 6° apart, on the line drawn 
from Arcturus through the head of Serpens, and produced 
as far again. Alpha Ophiuchi is the eastern and the 
brighter of the two, and forms with Vega and Altair a 
nearly equilateral triangle. Beta Ophiuchi lies about 9° 
southeast of Alpha. 

Five degrees east and a little south of Beta are five small stars in 
the Milky Way, forming a V with the point to the south, much like 
the Hyades of Taurus. They form the head of the now discredited 
constellation, " Poniatowski's Bull" (Taurus Poniatovil), proposed in 
1777, and found in many maps. 70 Ophiuchi (the middle star in 
the eastern leg of the V of Poniatowski's Bull) is a very pretty 
double star — binary — with a period of ninety-three years. Just at 
present the star is too close to be resolved by a small instrument. 

Kepler's "new star" of 1604 was situated in the left leg of 
Ophiuchus, between Eta and Theta. 

Ophiuchus is identified with iEsculapius, who was the first great 
physician, the son of Apollo and the nymph Coronis, educated in the 
art of medicine by Chiron, the Centaur. The serpent and the cock 
were sacred to him in his character as a deity. But the constellation 
is older than the classic legends. 






URANOGRAPHY 55 

66. Hercules (Maps I and IV). July This noble con- 
stellation lies next north of Ophiuchus, between it and 
Draco. The hero is represented as resting on one knee, 
with his foot on the head of Draco, while his head is close 
to that of Ophiuchus. The constellation contains no stars 
of the first or even of the second magnitude, but there are 
a number of the third. The most characteristic figure 
is the keystone-shaped quadrilateral formed by the stars 
Epsilon, Zeta, Eta, with Pi and Rho together at the north- 
east corner. It lies about midway on the line from Vega 
to Corona. 

On its western boundary, a third of the way from Eta towards 
Zeta, lies the remarkable cluster, Messier 13, — on the whole the 
finest of all star clusters in the northern hemisphere, — barely 
visible to the naked eye on a dark night. Alpha Herculis (Ras 
Algetlii), in the head of the giant, is a very beautiful double star; 
colors, orange and blue ; distance, about 5". It is also notably 
variable, and has a remarkable spectrum, characterized by numerous 
dark bands. 

Hercules, the son of Jupiter and Alcmena (a granddaughter of 
Andromeda), was the Greek incarnation of gigantic strength. His 
heroic actions and freaks occupy more space in their mythology than 
those of any personage except Jupiter himself. He was the pupil of 
Chiron, but by the will of Jupiter, his father, was subjected to the 
power of Eu^stheus, the king of Tiryns, for many years. At his 
bidding he performed the great enterprises known as the Twelve 
Labors of Hercules, for which we must refer the reader to the Clas- 
sical Dictionaries. Among them we have already mentioned the con- 
quest of the Nemsean Lion and of the Lerngean Hydra. Another 
was to bring from the garden of the Hesperides the golden apples 
which were guarded by the dragon that he killed, and on which his 
feet rest in the sky. His last and greatest achievement was to bring 
to the earth the three-headed dog, Cerberus, the guardian of the 
infernal regions. 



56 LESSONS IN ASTRONOMY 

67. Lyra (Map IV). August. — This constellation is 
sufficiently marked by the great white or blue star, Vega, 
one of the finest stars in the whole sky, and certainly many 
times larger than our own sun. It is attended on the east 
by two fourth-magnitude stars, Epsilon and Zeta, which 
form with it a little equilateral triangle having sides about 
2° long. Epsilon is a double-double or quadruple star. 
A sharp eye, even unaided by a telescope, divides the star 
into two, and a large telescope splits each of the compo- 
nents. It is a very pretty object even for a small telescope 
(Fig. 88). Beta and Gamma, of the third magnitude (Beta 
is variable), lie about 8° southeast from Vega, 2i° apart. 
(See Sec. 357.) 

On the line between Beta and Gamma, one-third of the way from 
Beta, lies Messier 57, the Annular Nebula, which can be seen as a 
small hazy ring even by a small telescope, though of course it is 
much more interesting with a larger one. 

According to the legends this constellation is the lyre of Orpheus, 
with which he charmed the stern gods of the lower world, and per- 
suaded them to restore to him his lost Eurydice. 

68. Cygnus (Maps I and IV). September. — This con- 
stellation lies due east from Lyra, and is easily recognized 
by the cross that marks it. The bright star Alpha (li 
magnitude) is at the top, and Beta (third magnitude) at 
the bottom, while Gamma is where the cross-bar from Delta 
to Epsilon intersects the main piece, which lies along the 
Milky Way from the northeast to the southwest. Beta 
(Albireo) is a beautiful double star, orange and dark blue, 
— one of the finest of the colored pairs for a small telescope. 
61 Cygni, which is memorable as the first star to have its 
parallax determined (by Bessel in 1838), is easily found by 



URANOGKAPHY 57 

completing the parallelogram of which Alpha, Gamma, and 
Epsilon are the other three corners. Sigma and Tau form 
a little triangle with 61, which is the faintest of the three. 
61 is a fine double star. Delta is also a fine double, but 
too difficult for an instrument of less than six inches 
aperture. 

According to Ovid, Cygnus was a friend of Phaethon's, who 
mourned his unhappy fate and was changed to a swan. Others see 
in the constellation the swan in whose form Jupiter visited Leda, 
the mother of Castor and Pollux and of Helen of Troy. 

69. Vulpecula et Anser, the Fox and the Goose (Map IV). 
September. — This little constellation is one of those originated by 
H evel ius and has obtained more general recognition among astrono- 
mers than most of his creations. It lies just south of Cygnus and is 
bounded to the south by Delphinus, Sagitta, and Aquila. It has no 
conspicuous stars, but it contains one very interesting telescopic 
object, — the "Dumb-bell Nebula," Messier 27. It may be found 
on a line from Gamma Lyrse through Beta Cygni, produced as far 
again. 

70. Sagitta (Map IV). August. — This little constellation, 
though very inconspicuous, is one of the old forty-eight. It lies 
south of Vulpecula, and the two stars Alpha and Beta, which mark 
the feather of the arrow, lie nearly midway between Beta Cygni and 
Altair, while its point is marked by Gamma, 5° farther east and 
north. Beta, the middle star of the shaft of the arrow, is a very 
pretty double star ; distance, about 8" : the larger star is itself a close 
double. 

71. A'quila (not Aquila) (Map IV). August. — This 
constellation lies on the celestial equator, east of Ophiu- 
chus and north of Sagittarius and Capricornus. Its charac- 
teristic configuration is that formed by Alpha (Altair), with 
Gamma to the north and Beta to the south. It lies about 
20° south of Beta Cygni and forms a fine triangle with 



58 LESSONS m ASTRONOMY 






Beta and Alpha Ophiuchi. Altair is taken as the standard 
first-magnitude star. Of course several of those which 
are ordinarily called first magnitude, like Sirius and Vega, 
are very much brighter than this, while others fall consid- 
erably below it. 

Aquila was the bird of Jupiter, which he kept by the side of his 
throne and sent to bring Ganymede to him. 

The southern part of the region allotted to Aquila on our maps has 
been assigned to Antinoiis, which is recognized on some celestial 
globes. The constellation existed even in Ptolemy's time, but he 
declined to adopt it. Hevelius appropriated the eastern part of 
Antinoiis for his constellation of Scutum Sobieski, which, however, is 
now seldom recognized. 

72. Sagittarius, the Archer (Map IV). August. — This, 
the tenth of the zodiacal constellations, contains no stars 
of the first magnitude, but a number of the second and 
third magnitude, which make it reasonably conspicuous. 
The most characteristic configuration is the little inverted 
" milk-dipper," formed by the five stars Lambda, Phi, 
Sigma, Tau, and Zeta, of which the last four form the 
bowl, while Lambda (in the Milky Way) is the handle. 
(See map.) Delta, Gamma, and Epsilon, which form a 
triangle, right-angled at Delta, lie south and a little west 
of Lambda, the whole eight together forming a very strik- 
ing group. There is a curious disregard of any apparent 
principle in the lettering of the stars of this constellation ; 
Alpha and Beta are stars not exceeding in brightness the 
fourth magnitude, about 4° apart on a north and south 
line, and lying some 15° south and 5° east of Zeta (see 
map), while Sigma is now a bright second-magnitude star, 
strongly suspected of being irregularly variable. The 



UKANOGRAPHY 59 

constellation contains an unusual number of known vari- 
ables. The Milky Way in Sagittarius is very bright and 
complicated in structure, full of knots and streamers and 
dark pockets, and containing many beautiful and inter- 
esting objects. 

This constellation is said by many writers to commemorate the 
Centaur, Chiron, but the same constellation appears on the ancient 
zodiacs of Egypt and India, and it seems probable, therefore, that, 
like the Bull and the Lion, it was not representative of any particular 
individual. 

73. Capricornus (Map IV). September. — This, the 
eleventh of the zodiacal constellations, follows Sagittarius on 
the east. It has no bright stars, but the configuration formed 
by the two Alphas (a x and a 2 ) with each other and with Beta, 
3° south, is characteristic, and not easily mistaken for any- 
thing else. The two Alphas, a pretty double to the naked 
eye, lie on the line drawn from Beta Cygni (at the foot 
of the cross) through Altair, and produced about 25°. 

Some say that this constellation represents the god Pan, who was 
represented by the Greeks as having the legs of a goat and the head 
of a man. Others find in the goat Amalthea (the foster-mother of 
the infant Jupiter), who is also, it will be remembered, represented 
in the constellation of Auriga. 

74. Delphinus, the Dolphin (Map IV). September.— 

This constellation, though small, is one of the ancient forty- 
eight and is unmistakably characterized by the rhombus of 
third-magnitude stars known as " Job's Coffin." It lies 
about 15° east of Altair. There are a few stars visible 
to the naked eye, in addition to the four that form the 
rhombus. Epsilon, about 3° to the southwest, is the only 
conspicuous one. 



60 LESSONS IN ASTRONOMY 

Gamma, at the northwest angle of the rhombus, is a very pretty- 
double star. Beta is also a very close and rapid binary, beyond the 
reach of all but large telescopes. 

This is the dolphin that preserved the life of the musician Arion, 
who was thrown into the sea by sailors, but carried safely to land 
upon the back of the compassionate fish, who loved his music. 

75. Equuleus, the Little Horse (Map IV). This little constella- 
tion, simply a horse's head, though still smaller than the Dolphin 
and less conspicuous, is also one of Ptolemy's. It lies about 20° due 
east of Altair, and 10° southeast of the Dolphin. (See map.) 

76. Lacerta, the Lizard (Maps I and IV). This is one of Heve- 
lius's modern constellations, lying between Cygnus and Andromeda, 
with no stars above the 4J magnitude, and of no importance for our 
purposes. 

77. Pe'gasus (not Pegas'us) (Map IV). October. — This 
winged horse covers an immense space. Its most notable 
configuration is the " great square," formed by the second- 
magnitude stars Alpha (Markab), Beta, and Gamma 
Pegasi, in connection with Alpha Andromedse (sometimes 
lettered Delta Pegasi) at its northeast corner. The stars 
of the square lie in the body of the horse, which has no 
hind quarters. A line drawn from Alpha Andromeda3 
through Alpha Pegasi, and produced about an equal dis- 
tance, passes through Xi and Zeta in the animal's neck 
and reaches Theta in his ear. Epsilon (Enif), the bright 
star 8° northwest of Theta, marks his nose. The fore legs 
are in the northwestern part of the constellation just east 
of Cygnus and are marked, one of them by the stars Eta and 
Pi, and the other by Iota and Kappa. 15 M. Pegasi is a fine 
cluster but little inferior to that in Hercules. 

Pegasus is the winged horse which sprang from the blood of 
Medusa, after Perseus had cut off her head. He fixed his residence 
on Mt. Helicon, where he was the favorite of the Muses, and after 



URANOGRAPHY 61 

being tamed by Minerva he was given to Bellerophon to aid him in 
conquering the ChimsBra. After the destruction of the monster, 
Bellerophon attempted to ascend to heaven upon Pegasus, but the 
horse threw off his rider and continued his flight to the stars. 

78. Aquarius, the Water-Bearer (Map IV). October. — 
This, the twelfth and last of the zodiacal constellations, 
extends more than 3i h in right ascension, covering a con- 
siderable region which by rights ought to belong to Capri- 
cornus. The most notable configuration is the little Y of 
third- and fourth-magnitude stars which marks the " water- 
jar*' from which Aquarius pours the stream that meanders 
down to the southeast and south for 30°, till it reaches 
the Southern Fish. The middle of the Y is about 18° 
south and west of Alpha Pegasi and lies almost exactly 
on the celestial equator. 

Zeta, the central star of the Y, is a pretty and interesting double 
star: distance, about 4". The "green nebula," nearly on the line 
from Alpha through Beta, produced about its own length, 1^° west 
of Xu, is a planetary nebula and curious from the vividness of its 
color. 

There are various opinions respecting the origin of this constel- 
lation. According to a Greek legend it represents Deucalion, the 
hero of the Greek Deluge : but among the Egyptians it evidently 
had reference to the rising and falling of the Xile. 

79. Piscis Austrinus (or Australis), the Southern Fish 
(Map IV). October. — This small constellation, lying 
south of Capricornus and Aquarius in the stream that 
issues from the Water-Bearer's urn, presents little of 
interest. It has one bright star, Fomalhaut (pronounced 
Fomal-haivt'), of the li magnitude, which is easily recog- 
nized from its being nearly on the same hour-circle with 
the western edge of the Great Square of Pegasus, 45° to 



62 LESSONS IN ASTRONOMY 

the south of Alpha Pegasi, and solitary, having no star 
exceeding the fourth magnitude within 15° or 20°. An 
incorrect pronunciation (Fomalo) is common; but "haut" 
is Arabic, not French. 

This constellation is by some said to represent the transformation 
of Venus into a fish, when fleeing from Typhon (but see Pisces), 

South of the Southern Fish, barely rising above the southern hori- 
zon, lie the constellations of Microscopium and Grus. The former is 
of no account. In the southern hemisphere Grus is a conspicuous 
constellation, and its two brightest stars, Alpha and Beta, of the 
second magnitude, rise high enough to be seen in latitudes south 
of Washington. They lie about 20° south and west of Fomalhaut. 



URANOGRAPHY 



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CHAPTER III 

LATITUDE, TIME, AND LONGITUDE 






Latitude, and the Aspect of the Celestial Sphere — Time — Longitude — The 
Place of a Heavenly Body 

80. Latitude defined. — In Geography the latitude of a 
place is usually defined simply as its distance north or 
south of the equator, measured in degrees. This is not 
explicit enough, unless it is stated how the degrees them- 
selves are to be measured. There would be no difficulty 
if the earth were a perfect sphere ; but since the earth 
is a little flattened at the poles, the degrees (geographical) 
are of somewhat different lengths at different parts of 
the earth. The exact definition of the astronomical lati- 
tude of a place is the angle between the direction of the 
observers plumb-line and the plane of the earth's equator; 
and this is the same as the altitude, or angle of elevation, 
of the pole, as will be clear from Fig. 7. Here the angle 
ONQ is the latitude as defined. If now at we draw 
HH 1 perpendicular to OZ, it will be a level line, and will 
point to the horizon. From also draw OP n , parallel to 
CP ! , the earth's axis. Since OP 1 and CP n are parallel, 
they will be directed apparently to the same point in the 
celestial sphere (Sec. 6), and this point is the celestial 
pole. The angle H 1 OP n is therefore the altitude of the 
pole, as seen at 0, and it obviously equals ONQ ; and this 
is true whether the earth be a sphere, or whatever its 

64 



LATITUDE 



65 



form. This fundamental relation, that the Altitude of the 
Pole is Identical with the Observer's Latitude, cannot be 
too strongly impressed on the mind. 

81. Method of measuring the Latitude. — The most obvi- 
ous method is to observe, with a suitable instrument, the 
altitude of some star near the pole (a " circumpolar " star) 
at the moment when 

it is crossing the me- Z 

ridian above the pole, 
and again twelve hours 
later, when it is once 
more on the meridian 
below the pole. In the 
first position its eleva- 
tion is the greatest pos- 
sible ; in the second, 
the least. The average 
of these two altitudes, FlG ' 7 
when corrected for re- 
fraction, is the latitude of the observer. It is exceedingly 
important that the student understand this simple method 
of determining the latitude. 

The instrument ordinarily used for making observations of this 
kind at an observatory is called a meridian circle, and a brief descrip- 
tion is given in the Appendix. (See Sec. 418.) 

82. Refraction. — When we observe the altitude of a 
heavenly body with any instrument we do not find it the 
same that it would be if our atmosphere had no effect 
upon the rays of light. As they enter the earth's atmos- 
phere they are bent downward by " refraction," excepting 
only such as come from exactly overhead. Since the 




- Relation of Latitude to the Elevation 
of the Pole 



66 LESSONS m ASTRONOMY 

observer sees the object in the direction in which the rays 
enter the eye, without any reference to its real position, this 
bending down of the rays causes every object seen through 
the air to look higher up in the shy than it would be if the 
air were absent; and we must therefore correct the observed 
altitude by subtracting the proper amount. Under ordinary 
conditions, refraction elevates a body at the horizon about 
35', so that the sun and moon in rising appear clear of the 
horizon while they are still wholly below it. The refraction 
correction diminishes very rapidly as the body rises. At 
an altitude of only 5° the refraction is but 10'; at 44°, 
it is about V ; and at the zenith, zero, of course. 

Its amount at any given time is affected quite sensibly, however, 
by the temperature and by the height of the barometer, increasing 
as the thermometer falls or as the barometer rises ; so that whenever 
great accuracy is required in measures of altitude we must have 
observations of both the barometer and thermometer to go with the 
reading of the circle. There are tables by which the refraction can 
be computed for an object at any altitude and in any state of the 
weather. But this indispensable correction is very troublesome, and 
always involves more or less error. 

(For other methods of determining the latitude, see 
Appendix, Sec. 424.) 

83. Effect of the Observer's Latitude upon the Aspect of 
the Heavens ; the Right Sphere. — If the observer is situ- 
ated at the earth's equator, — i.e., in latitude zero, — the 
celestial poles will evidently be on the horizon, and the 
celestial equator will pass through the zenith and coincide 
with the prime vertical (Sec. 11). At the earth's equator, 
therefore, all heavenly bodies will rise and set vertically, 
and their diurnal circles will be equally divided by the 



ASPECT OF THE HEAVENS 



67 



horizon, so that they will be twelve hours above it and 
twelve hours below it, and the length of the night will 
always equal that of the day. This aspect of the heavens 
is called the right sphere. 

84. Parallel Sphere. — If the observer is at one of the 
poles of the earth, where the latitude equals 90°, then the 
corresponding celestial pole will be exactly overhead, and 
the celestial equator will coincide with the horizon. If he 
is at the north pole, all 
the stars north of the 
celestial equator will re- 
main permanently visible, 
never rising or setting, 
but sailing around the sky 
on parallels of altitude, 
while the stars south of 
the equator will never rise 
to view. Since the sun 
and the moon move in 
such a way that during 
half the time they are 
north of the equator and 




Fig. 8. — The Oblique Sphere 



half the time south of it, they will therefore be half the 
time above the horizon and half the time below it (that is, 
approximately, since refraction has a noticeable effect). 
The moon will be visible for about a fortnight at a time, 
and the sun for about six months. 

85. The Oblique Sphere. — At any station between the 
pole and the equator the pole will be elevated above the 
horizon, and the stars will rise and set in oblique circles, 
as shown in Fig. 8. Those stars whose distance from the 



68 LESSONS IN ASTRONOMY 

elevated pole is less than PiV, the latitude of the observer, 
will never set, the radius of this circle of perpetual appa- 
rition being just equal to the altitude of the pole, and 
becoming larger as the latitude increases. On the other 
hand, stars within the same distance of the depressed pole 
will lie within the circle of perpetual occultation, and will 
never, rise above the observer's horizon. An object which 
is exactly on the celestial equator will have its diurnal 
circle, EQ WQ 1 , equally divided by the horizon, and will be 
above the horizon just as long as below it. 

For an observer in the United States a star north of the 
equator will have more than half of its diurnal circle above 
the horizon, and jrill be visible for more than twelve hours 
of each day ; as, for instance, the star at A. Whenever 
the sun is north of the celestial equator the day will there- 
fore be longer than the night for all stations in northern 
latitude ; how much longer will depend both on the latitude 
of the place and the sun's distance from the equator (the 
sun's declination). 

86. Moreover, when the sun is north of the equator, it 
will, in the northern latitudes, rise at a point north of east, 
as at B in the figure, and will continue to shine, on the 
north side of every wall that runs east and west until, as 
it ascends, it crosses the prime vertical, EZW, at some 
point, as V. In the latitude of New York the sun in June 
is south of the prime vertical for only about eight hours 
of the whole fifteen during which it is above the horizon. 
During seven hours of the day, therefore, it shines into 
north windows. 

If the latitude of the observer is such that PiV, in the 
figure, is greater than the sun's polar distance at the time 



TIME 69 

when it is farthest north, the sun at midsummer will make 
a complete circuit of the heavens without setting, thus 
producing the phenomenon of the " midnight sun," visible 
at the North Cape and at all stations within the Arctic 
Circle. 

87. A celestial globe will be of great use in studying 
these diurnal phenomena. The north pole of the globe 
must be elevated to an angle equal to the latitude of the 
observer, which can be done by means of the degrees marked 
on the metal meridian ring. It will then be seen at once 
what stars never set, which ones never rise, and during 
what part of the twenty-four hours any heavenly body at 
a known distance from the equator is above or below the 
horizon. (For description of the celestial globe, see Appen- 
dix, Sec. 400.) 

TIME 

Time is usually defined as " measured duration," and 
the standard unit of time has always been obtained in some 
way from the length of the day. 

88. Apparent Solar Time. — The most natural way, since 
we are obliged to regulate our lives by the sun, is to reckon 
time by him ; i.e., to call it noon when the sun is on the 
meridian and highest, and to divide the day from one noon 
to another into its hours, minutes, and seconds. Time 
thus reckoned is called apparent solar time (see Appendix, 
Sec. 422), and is the time shown by a correctly adjusted 
sundial. But because the sun's eastward motion in the 
sky is not uniform (owing to the oval form of the earth's 
orbit and its inclination to the equator), these apparent 
solar days are not exactly of the same length. Thus, for 



70 LESSONS IN ASTRONOMY 

instance, the interval from noon of December 22 to noon 
of December 23 is nearly a minute longer than the inter- 
val between the noons of September 15 and 16. As a con- 
sequence, it is only by very complicated and expensive 
machinery that a watch or clock can be made to keep time 
precisely with the sundial; nor is it worth while, since 
it is much better to have the timekeeper uniform in its 
motion. Apparent solar time is now used only in commu- 
nities where clocks and watches are rare and sundials are 
the usual timepieces, as in China and in much of the East. 

89. Mean Solar Time. — At present, for civil and busi- 
ness purposes, time is almost universally reckoned in days 
all of which have precisely the same length, and are just 
equal to the average apparent solar day; and this time, 
called mean solar time (Appendix, Sec. 422), is that which 
is kept by all good timepieces. 

Sundial time agrees with mean time four times a year; viz., upon 
April 15, June 14, September 1, and December 24. The greatest 
differences occur on November 2 and February 11, when the sundial 
is respectively 16 m 20 s fast of the clock and 14 m 30 s slow. During 
the summer the difference never exceeds 6 m . This variable differ- 
ence is called the Equation of Time, and is given in the almanac for 
every day in the year. 

90. The Civil Day and the Astronomical Day. — The astronomical 
day begins at noon ; the civil day at midnight, twelve hours earlier. 
Astronomical mean time is reckoned around through the whole 
twenty -four hours, instead' of being counted in two series of twelve 
hours each. Thus, 8 a.m. of Tuesday, August 12, civil reckoning, 
is Monday, August 11, 20 h , of astronomical reckoning. Beginners 
need to bear this in mind in referring to the almanac. 

91. Sidereal Time, or Time reckoned by the Stars. — As 
lias been said (Sec. 17), the sun is not fixed on the celestial 



DETERMINATION OF TIME 71 

sphere, but appears to creep completely around it once 
a year, moving daily about one degree eastward among the 
stars. The interval from noon to noon does not therefore 
correspond to the true diurnal revolution of the heavens. 
If we reckoned by the interval between two successive 
passages of any given star across the observer's meridian, 
we should find that this true day, the sidereal day, as it 
is called, is nearly 4 m shorter (3 m 56 s .9) than the ordinary 
solar day, from noon to noon the relation being such that 
in a year the number of sidereal days exceeds that of solar by 
exactly one. For many purposes, astronomers find it much 
more convenient to reckon by the stars than by the sun. 
They count the time, however, not by any real star, but 
from the Vernal Equinox, the sidereal clock being so set 
and regulated that it always shows zero hours, minutes, 
and seconds (sidereal noon) at the moment when the vernal 
equinox is on the meridian. (See Appendix, Sec. 422.) 

This kind of time, of course, would not answer for busi- 
ness purposes, since its noon comes at all hours of the day 
and night at different seasons of the year. The almanac 
gives data by which sidereal time and mean solar time can 
be easily converted into each other. 

92. The Determination of Time. — In practice, the 
problem always takes the shape of finding the error of a 
timepiece of some sort ; i.e., ascertaining how many seconds 
it is fast or slow. The instrument now ordinarily used 
for the purpose is the transit instrument, which is a small 
telescope mounted on an axis, placed exactly east and 
west, and level, so that as the telescope is turned it will 
follow the meridian ; at least, the middle cross-wire in the 
field of view will do so. It is the same as the meridian 



72 LESSONS IN ASTRONOMY 

circle, except that it does not require the costly graduated 
circle with its appendages. (For description, see Appendix, 
Sec. 416.) 

To determine with the transit the error of the sidereal 
clock which is ordinarily used in connection with it, it is 
only necessary to observe the exact time indicated by the 
clock when some star whose right ascension is known 
passes, or " transits," the middle wire of the instrument. 

93. The right ascension of a star (Sec. 18) is the num- 
ber of " hours " of arc (measured along the equator) by which 
the star is east of the vernal equinox ; and therefore when the 
star is on the meridian the right ascension also equals the 
number of hours, minutes, and seconds since the transit 
of the vernal equinox . In other words, we may say that 
the right ascension of a star is the local sidereal time at the 
moment of its meridian transit. (This is often called the 
observatory definition of right ascension.) For instance, 
the right ascension of Vega (Alpha Lyrse) is 18 h 33 m . If 
we observe its transit to occur at 18 h 40 m by the clock, the 
clock is obviously 7 m fast. 

With a good instrument, a skilled observer by observing 
a number of stars can thus determine the clock-error 
within about one-thirtieth of a second of time. 

To get solar time, we may observe the sun itself, the 
moment of its transit being " apparent noon." But it is 
better, and it is usual, to get the sidereal time first, and to 
deduce from that the solar time by means of the necessary 
data which are furnished in the almanac. 

The method by the transit instrument is most used, and is, on the 
whole, the most convenient ; but since the instrument requires to be 
mounted upon a firm pier, it is not always available. When not, we 



LONGITUDE 73 

use some one of various other methods, for which reference must be 
made to the General Astronomy. At sea, and by travelers on scientific 
expeditions, the time is usually determined by observing the altitude 
of the sun with a sextant some hours before or after noon. (See 
Appendix, Sec. 427.) 

LONGITUDE 

94. The problem of finding the longitude is in many 
respects the most important of what may be called the 
"econoinic" problems of Astronomy; i.e., those of business 
utility to mankind. The great observatories of Greenwich 
and Paris were founded for the express purpose of fur- 
nishing the necessary data to enable the sailor to determine 
his longitude at sea; and the English government has 
given great prizes for the construction of clocks and chro- 
nometers fit to be used in such determinations. 

The longitude of a place on the earth is defined as the 
arc of the equator intercepted between the meridian which 
passes through the place and some meridian which is taken 
as the standard. 1 

Now, since the earth turns on its axis at a uniform rate, 
this arc is strictly proportional to, and may be measured by, 
the interval of sidereal time between the transits of a given 
star across the two meridians, or by the interval of mean 
solar time between the transits of the sun. The longitude 
of a place may therefore be defined as the amount by which 
the time at Greenwich is earlier or later than the time at the 
station of the observer, and this whether we reckon by solar 
or by sidereal time. Accordingly, terrestrial longitude is 

1 As to the standard meridian, there is a variation of usage among dif- 
ferent nations. The French reckon from the meridian of Paris, but most 
other nations use the meridian of Greenwich, at least at sea. 



74 LESSONS m ASTRONOMY 

usually reckoned in hours, minutes, and seconds, rather 
than in degrees. Since the observer can easily find his 
own local time by the transit instrument, or by some of 
the many other methods, the knot of the problem is simply 
this : to find the Greenwich time at any moment without 
going to Greenwich; then we get the longitude at once 
by simply comparing it with our own time. 

95. Methods of determining Longitude. — Incomparably 
the best method, whenever it is available, is to make a 
direct telegraphic comparison between the clock of the 
observer and that of some station the longitude of which 
is known. The difference between the two clocks, duly 
corrected for their " errors " (Sec. 92), will be the true dif- 
ference of longitude. The astronomical difference of longi- 
tude between the two places can thus be determined by 
four or five nights' observations within about S .02, i.e., 
within twenty feet or so, in the latitude of the United 
States. In many cases the telegraphic method, however, 
is not available; never at sea, of course, unless perhaps 
the " wireless telegraph " may sometime make it possible. 

96. A second method is to use a chronometer, which is 
simply a very accurate watch. This is set to Greenwich 
time at some place whose longitude is known, and after- 
wards is supposed to keep that time wherever carried. 
The observer has only to compare his own local time, 
determined with the transit instrument or sextant, with 
the time shown by such a chronometer, and the difference 
is his longitude from Greenwich. This is the ordinary 
method at sea. 

Practically, of course, no chronometer goes absolutely without 
gaining or losing ; hence, it is always necessary to know and to 



LOCAL AND STANDARD TIME 75 

allow for its gain or loss since the time it was last set. Moreover, it 
is never safe to trnst a single chronometer, because of the liability of 
such instruments to change their rate in transportation. A number 
(three or more) should be used, if possible. 

Before the days of telegraphs and chronometers, astrono- 
mers were generally obliged to get their Greenwich time 
from the moon, which may be regarded as a clock-hand 
with the stars for dial figures; but observations of this 
kind are troublesome, and the results inaccurate as com- 
pared with those obtained by the telegraph and chronom- 
eter. (For further details, see General Astronomy, 
Arts. 109-116.) 

97. Local and Standard Time. — Until recently it has 
been always customary to use local time, each station 
determining its own time by its own observations, and 
having, therefore, a time differing from that of all other 
stations not on the same meridian. Before the days of 
the telegraph, and while traveling was comparatively 
slow, this was best. At present there are many reasons 
why it is better to give up the old system in favor of a 
system of standard time. The change greatly facilitates 
all railway and telegraphic business, and makes it practi- 
cally easy for everybody to have accurate time, since the 
standard time can be daily wired from some headquarters 
to every telegraph office. 

According to the system now established in North 
America, there are five such standard times in use, — the 
colonial, the eastern, the central, the mountain, and the 
Pacific, — which differ from Greenwich time by exactly 
four, five, six, seven, and eight hours respectively, the 
minutes and seconds being everywhere identical, and the 



76 LESSONS IN ASTRONOMY 

same with those of the clock at Greenwich. In order to 
determine the standard time by observation, it is neces- 
sary only to find the local time by one of the methods 
given and correct it according to the observer's longitude 
from Greenwich. 

98. Where the Day begins. — It is clear that if a trav- 
eler were to start from Greenwich on Monday noon, and 
travel westward as fast as the earth turns to the east 
beneath his feet, he would have the sun upon the meridian 
all day long, and it would be continual noon. But what 
noon? It was Monday when he started, and when he 
gets back to London twenty-four hours later it will be 
Tuesday noon there, and yet he has had no intervening 
night. When did Monday noon become Tuesday noon? 

It is agreed among mariners to make the change of 
date at the 180th meridian from Greenwich. Ships cross- 
ing this line from the east skip one day in so doing. If 
it is Monday afternoon when a ship reaches the line, it 
becomes Tuesday afternoon the moment she passes it, the 
intervening twenty-four hours being dropped from the 
reckoning on the log-book. Vice versa, when a vessel 
crosses the line from the western side it counts the same 
day twice, passing from Tuesday back to Monday. 

This 180th meridian passes mainly over the ocean, hardly touch- 
ing land anywhere. There is some irregularity as to the date actually 
used on the different islands of the Pacific. Those which received 
their earliest European inhabitants via the Cape of Good Hope have, 
for the most part, adopted the Asiatic date, even if they really lie 
east of the 180th meridian, while those which were first approached 
via Cape Horn have the American date. When Alaska was trans- 
ferred from Russia to the United States it was necessary to drop 
one day of the week from the official dates. 



PLACE OF A CELESTIAL OBJECT 77 

DETERMIXATIOX OF THE POSITION OF A 
HEAVENLY BODY 

As the basis of our investigations in regard to the 
motions of the heavenly bodies, we require a knowledge 
of their places in the sky at known times. By determin- 
ing the " place " of a body, we mean finding its right 
ascension and declination. 

99. By the Meridian Circle (see Appendix, Sec. 418). — 
If a body is bright enough to be seen by the telescope of the 
meridian circle, and comes to the meridian in the nighttime, 
its right ascension and declination are best determined by 
the Meridian Circle. If the instrument is in exact adjust- 
ment, the right ascension of the body is simply the sidereal 
time when it crosses the middle vertical wire of the reticle. 
The " circle-reading," on the other hand, corrected for 
refraction, gives the declination. A single complete obser- 
vation with the meridian circle determines accurately both 
the right ascension and the declination of the object. 

100. By the Equatorial. — If the body — a comet, for 
instance — is too faint to be observed by the telescope of 
the meridian circle, seldom very powerful, or comes to the 
meridian only in the daytime, we usually accomplish our 
object by using the equatorial (Appendix, Sec. 414), and 
determine the position of the body by measuring with 
some kind of " micrometer " the difference of right ascen- 
sion and declination between it and a neighboring star 
whose place is given in some star-catalogue. 



CHAPTER IV 

THE EARTH 






Its Form and Dimensions ; its Rotation, Mass, and Density ; its Orbital 
Motion and the Seasons — Precession — The Year and the Calendar 

101. In a science which deals with the "heavenly 
bodies," there might seem at first to be no place for the 
Earth. But certain facts relating to the Earth, just such 
as we have to investigate with respect to her sister planets, 
are ascertained by astronomical methods, and a knowledge 
of them is essential as a base of operations. In fact, Astron- 
omy, like charity, " begins at home," and it is impossible to 
go far in the study of the bodies which are strictly " heav- 
enly " until we have first acquired some accurate knowledge 
of the dimensions and motions of the earth itself. 

102. The astronomical facts relating to the earth are 
broadly these : 

1. The earth is a great ball about 7920 miles in diameter. 

2. It rotates on its axis once in twenty-four " sidereal " 
hours. 

3. It is not exactly spherical, but is slightly flattened at 
the poles ; the polar diameter being nearly twenty-seven 
miles, or about g-l_ part less than the equatorial. 

4. It has a mean density of about 5.5 times that of 
water, and a mass represented in tons by 6 with twenty- 
one ciphers following (six thousand millions of millions of 
millions of tons). 

78 



THE EARTH 79 

5. It is flying through space in its orbital motion around 
the sun, with a velocity of about eighteen and a half miles 
a second; i.e., about seventy-five times as swiftly as an 
ordinary cannon-ball. 

103. The Earth's Approximate Form and Size It is 

not necessary to dwell on the ordinary proofs of the globu- 
larity of the earth. We simply mention them. 

1. It can be sailed around. 

2. The appearance of vessels coming in from the sea 
indicates that the surface is everywhere convex. 

3. The fact that as one goes from the equator towards 
the north the elevation of the pole increases in proportion 
to the distance from the equator, proves the same thing. 

4. The outline of the earth's shadow, as seen upon the moon 
during lunar eclipses, is such as only a sphere could cast. 

We may add, as to the smoothness and roundness of the 
earth, that if the earth be represented by an eighteen-inch 
globe, the difference between its greatest and least diam- 
eters would be only about one-sixteenth of an inch; the 
highest mountains would project only about one-ninetieth 
of an inch, and the average elevation of continents and 
depths of the ocean would be hardly greater than a film 
of varnish. Relatively, the earth is really much smoother 
and rounder than most of the balls in a bowling-alley. 

104. One of the simplest methods of showing the curvature of 
the earth is the following : 

In an expanse of still, shallow water (a long reach of canal, for 
instance) set a row of three poles about a mile apart, with their 
tops projecting to exactly the same height above the surface. On 
sighting across, it will then be found that the middle pole projects 
above the line that joins the tops of the two end ones, and from the 
amount of this projection, after due correction for refraction (which 



80 



LESSONS m ASTRONOMY 






reduces it from about eight inches to six under ordinary conditions 
of temperature), a rough estimate of the size of the earth can be 
made. (See General Astronomy, Art. 134.) 

105. Measure of the Earth's Diameter. — The only accu- 
rate method of measuring the diameter of the earth is the 
following, the principle of which is very simple, and should 

be thoroughly mastered by the 
student : 

It consists in finding the 
length in miles of an arc of 
the earth's surface containing a 
known number of degrees. From 
this we get the length of one 
degree, and this gives the circum- 
ference of the earth (since it 
contains 360°), and from this the 
diameter is obtained by dividing 
it by 3.14159. 

To do this, we select two 
stations, a and b (Fig. 9), some 
hundreds of miles apart on the 
same meridian, and determine 

Fig. 9. -Measuring the Earth's the latitude (or the altitude of 

Diameter x 

the pole) at each station by 
astronomical observation. The difference of latitude (i.e., 
ECb — ECa) is evidently the number of degrees in the arc 
ab, and the determination of this difference of latitude 
is the only astronomical operation necessary. 

Next, the distance in miles between the two stations 
must be measured. This is geodetic work, and it is 
enough for our purpose here to say that it can be 




THE EARTH'S ROTATION 81 

done with great precision by a process which is called 
" triangulation." 

This measurement of arcs has been made on many parts 
of the earth's surface, and the result is that the average 
length of a degree is found to be a little more than sixty- 
nine miles, and the mean diameter of the earth about 
7918 miles. The reason why we say average length and 
mean diameter is that the earth, as has been said, is not 
quite spherical, but is slightly flattened at its poles, so 
that the lengths of the degrees differ in different parts of 
the earth, as we shall soon see (Sec. 110). 

106. The Rotation of the Earth. — Ptolemy understood 
that the earth was round, but he and all his successors 
deliberately rejected the theory of its rotation. Though 
the idea that the earth might turn upon an axis was not 
unfamiliar, they considered that there were conclusive 
reasons against it. At the time when Copernicus of Thorn, 
in Poland (1473-1543), proposed his theory of the solar 
system, the only argument he could urge in favor of the 
earth's rotation 1 was that this hypothesis was much more 
probable than the older one that the heavens themselves 
revolve. All the phenomena then known would be sen- 
sibly the same on either supposition. The apparent daily 
motion of the heavenly bodies can be perfectly accounted 
for (within the limits of such observations as were then 
possible) either by supposing that they are actually attached 
to the celestial sphere, which turns daily, or that the earth 

1 The word "rotation " denotes a spinning motion, like that of a wheel 
on its axis. The word "revolve" is more general, and may be used to 
describe such a spinning motion or (and this is the more common use in 
Astronomy) to describe the motion of a body traveling around another, 
as when we say the earth " revolves " around the sun. 



82 



LESSONS IN ASTRONOMY 



itself spins upon an axis once in twenty-four hours ; and 
for a long time the latter hypothesis did not seem to most 
people so reasonable as the older and more obvious one. 
A little later, after the telescope had been invented, analogy 
could be appealed to ; for we can see with the telescope 
that the sun and moon and many of the planets really 
rotate upon axes. At present we can go still further, and 

can absolutely demon- 
strate the earth's rota- 
tion by experiments, 
some of which even 
make it visible. 

107. Foucault's Pen- 
dulum Experiment. — 
Among these experi- 
mental proofs the most 
impressive is the " pen- 
dulum experiment" 
devised by Foucault in 
1851. From the dome 
of the Pantheon, in 
Paris, he hung a heavy 
iron ball by a slender 
wire more than 200 feet 
long (Fig. 10). A circular rail, with a little ridge of sand 
built upon it, was placed in such a way that a pin attached 
to the swinging ball would just scrape the sand and leave 
a mark at each vibration. To put the ball in motion, it was 
drawn aside by a cotton cord and left for some hours, until 
it came absolutely to rest. Then the cord was burned off, 
and the pendulum started to swing in a true plane. 



,d 




Fig. 10. — Foucault's Pendulum in the 
Pantheon 



THE EARTH'S ROTATION 83 

But this plane at once began to deviate slowly towards 
the right, so that the pin on the pendulum ball cut the 
sand ridge in a new place at each swing, shifting at a rate 
which would carry the line fully around in about thirty- 
two hours, if the pendulum did not first come to rest. In 
fact, the floor was actually and visibly turning under the 
plane defined by the swinging of the pendulum. 

The experiment created great enthusiasm at the time and has since 
been frequently performed (in Paris, very recently). The pendulum 
used in such experiments must, in order to secure success, have a 
round ball, must be suspended by a round wire or on a point, and 
must be very heavy, very long, and very carefully protected against 
currents of wind. At the pole the plane of the pendulum will shift 
completely around once in twenty-four hours ; at the equator it will 
not turn at all; and in the intermediate regions it will shift more 
or less rapidly according to the latitude of the place where the 
experiment is performed. (For fuller description, see General 
Astronomy, Arts. 140 and 141.) 

There are a number of other experimental proofs of the earth's 
rotation, which are really just as conclusive as the one above cited 
(General Astronomy, Arts. 138-144). 

108. Invariability of the Earth's Rotation. — It is a 

question of great importance whether the day ever changes 
its length. Theoretically, it must almost necessarily do so. 
The friction of the tides and the fall of meteors upon the 
earth both tend to retard the rotation, while, on the other 
hand, the earth's loss of heat by radiation and the conse- 
quent shrinkage of the globe must tend to accelerate it, 
and to shorten the day. Then geological changes, the 
elevation and subsidence of continents, and the transporta- 
tion of soil by rivers, act, some one way and some the 
other. At present we can only say that the change, if any 



84 



LESSONS IN ASTRONOMY 






change has occurred since Astronomy became accurate, has 
been too small to be detected. The day is certainly not 
longer or shorter by the ^1^ part of a second than it was 
in the days of Ptolemy; probably it has not changed by 
the yoVo P ar t of a second, though of that we can hardly 
be sure. 

109. Shif tings of the Earth's Axis. — Theoretically, any changes 
in the distribution of materials within or upon the globe of the earth 
ought to produce corresponding displacements of the axis, and these 

would principally show 
themselves as variations in 
the latitudes and longitudes 
of observatories. The actual 
variations are so minute, 
however, that it is only as 
recently as 1889 that they 
were first clearly detected by 
certain German observers, 
whose results have since been 
abundantly confirmed and 
extended. It is now beyond 
doubt that the earth really 
" wobbles " in whirling; and 
this causes each pole to describe an apparently irregular path around 
its mean position, never departing from it, however, by more than 
forty or fifty feet. Dr. Chandler has shown that this motion is com- 
pounded of two : one oval, with a period of a year ; the other circular, 
with a period of 428 days. 

To explain certain geological phenomena it has been surmised that 
great and permanent displacements of the poles have occurred in the 
distant past. But of this we have, as yet, no satisfactory evidence. 

110. Effect of the Earth's Rotation on its Form. — The 

whirling of the earth on its axis tends to make the globe 
bulge at the equator and flatten at the poles, in the way 




Fig. 11.- 



- Effect of Earth's Rotation on its 
Form 



THE EARTH'S FORM 



85 



illustrated by the well-known little apparatus shown in 
Fig. 11. That the equator does really bulge in this way 
is shown by measuring the leyigth of a degree of latitude 
on the various parts of the earth's surface betiveen the equator 
and the pole, in the manner indicated a few pages back 
(Sec. 105). More than twenty such arcs have been meas- 
ured, and it appears that the length of the degrees increases 
regularly from the equator towards the poles, as shown in 
the following table : 



At the equator, 


one 


degree 


= 68.704 miles. 


At lat. 20° 


a 




= 68.786 « 


u a 4QO 


a 




= 68.993 « 


" " 60° 


a 




= 69.230 « 


" " 80° 


u 




= 69.386 « 


At the pole, 


u 




= 69.407 « 



The difference between the equatorial and polar degree 
of latitude is more than 0.7 of a mile, or over 3700 feet, 
while the probable error of measurement cannot exceed a 
foot or two to the degree. 

From this table it can be calculated, by methods which 
cannot be explained without assuming too much mathe- 
matical knowledge in our readers, that the earth is orange- 
shaped, or "an oblate spheroid," the diameter from pole 
to pole being 7899.74 miles, while the equatorial diameter 
is 7926.61 miles. The difference, 26.87 miles, is about -g^- 
of the equatorial diameter. This fraction, 3^, is called 
the oblateness, or ellipticity, of the earth. 

Scholars are often puzzled by the fact that although the pole is 
nearer the center of the earth than the equator, yet the degrees of 
latitude are longest at the pole. It is because the earth's surface 



86 



LESSONS m ASTRONOMY 



there is more nearly flat than anywhere else, so that a person has to 
travel more miles to change the direction of his plumb-line one 
degree. Fig. 12 illustrates this. The angles adb and fhg are equal, 
but the arc ab is longer than fg. 

111. Effect of the Earth's Rotation and Ellipticity upon 
the Force of Gravity. — For two reasons the force of gravity 
is less at the equator than at the poles. (1) The surface 
of the earth is there thirteen and one-half miles farther 
from the center, and this fact diminishes the gravity at 
the equator by about ^^. (2) The centrifugal force of 

the earth's rotation 
reduces the gravity 
at the equator by 
about 2¥ 9 ' th e 
whole reduction, 
therefore (^1^ + 
2^9), is very nearly 
equal to -jl^ ; i.e., 
an object which 
weighs 190 pounds 
at the equator 
would weigh 191 pounds near the pole, — weighed by an 
accurate spring-balance. (In an ordinary balance the loss 
of weight would not show, simply because the weights 
themselves would be affected as much as the body weighed, 
so that the balance would not be disturbed.) 

The effect of this variation of gravity from the pole to the 
equator is especially evident in the going of a pendulum 
clock. Such a clock, adjusted to keep accurate time at the 
equator, would gain 3 m 37 s a day near the pole. In fact, 
one of the best ways of determining the form of the earth 




Fig. 12. — Length of Degrees in Different 
Latitudes 



THE EARTH'S MASS AND DENSITY 87 

is by experiments with a pendulum at stations which differ 
considerably in latitude. 

112. Surface and Volume of the Earth. — The earth is 
so nearly spherical that we can compute its surface and 
volume with sufficient accuracy by the formula for a per- 
fect sphere, provided we put the earth's mean semi-diameter 
for the radius of the sphere. This mean semi-diameter is 
not the average of the polar and equatorial diameters, but 
is found by adding the polar diameter to twice the equa- 
torial, and dividing by three. It comes out 7917.66 miles. 
From this we find the earth's surface to be, in round num- 
bers, 197,000p00 square miles, and its volume, or bulk, 
260,000,000,000 cubic miles. 

113. The Earth's Mass and Density. — The volume (or 
bulk) of a globe is simply the number of cubic miles of 
space which it contains. If the earth were all made of 
feathers or of lead, its volume would remain the same, as 
long as the diameter was not altered. The earth's mass, 
on the other hand, is the quantity of matter in it, — the 
number of tons of rock and water which compose it, — and 
of course it makes a great difference with this whether the 
material be heavy or light. The density of the earth is the 
number of times its mass exceeds that of a sphere of pure 
water having the same dimensions. 

The methods by which the mass of the earth can be measured 
depend upon a comparison between the attraction which the earth 
exerts upon a body at its surface and the attraction which is exerted 
upon the same body by another body of known mass and at a known 
distance. The necessary experiments are delicate and difficult, 
because the attraction exerted by a body of any manageable size 
is extremely minute. We must refer for details to our larger 
book, General Astronomy, Arts. 164-170. 



88 LESSONS IN ASTRONOMY 






According to the best data at present available the earth's 
density is about 5.53, and its mass about 6000 millions of 
millions of millions of tons. 

Among the recent determinations the most trustworthy 
perhaps are those made by Boys in England in 1894, and 
by Braun in Bohemia about the same time. 

114. Constitution of the Earth's Interior. — Since the 
average density of the earth's crust does not exceed three 
times that of water, while the mean density of the whole 
earth is about 5.53, it is clear that at the earth's center the 
density must be very much greater than at the surface. 
Very likely it is as high as eight or ten times the density 
of water, and equal to that of the heavier metals. 

There is nothing surprising in this. If the earth were once fluid, 
it is natural to suppose that the densest materials, in the process of 
solidification, would settle towards the center. 

Whether the center of the earth is now solid or fluid, it is difficult 
to say with certainty. Certain tidal phenomena, to be mentioned 
hereafter, have led Sir William Thomson to conclude that the earth 
as a whole is solid throughout, and " more rigid than glass," vol- 
canic centers being mere " pustules/' so to speak, in the general 
mass. To this most geologists demur, maintaining that at the 
depth of not many hundred miles the materials of the earth must 
be fluid, or at least semi-fluid. They infer this from the phenomena 
of volcanoes, and from the fact that the temperature continually 
increases with the depth, so far at least as we have yet been able to 
penetrate. 



EARTH'S ORBITAL MOTION 89 

THE APPARENT MOTION OF THE SUN AND THE 

ORBITAL MOTION OF THE EARTH, AND THEIR 

IMMEDIATE CONSEQUENCES 

115. The Sun's Apparent Motion among the Stars. — The 
sun's apparent motion among the stars, 1 which makes it 
describe the circuit of the heavens once a year, must have 
been among the earliest recognized astronomical phenomena, 
as it is one of the most important. The sun, starting in 
the spring, mounts northward in the sky each day at noon 
for three months, appears to stand still a few days at the 
summer solstice, and then descends towards the south, reach- 
ing in autumn the same noonday elevation which it had in 
the spring. It keeps on its southward course to the winter 
solstice (in December), and then returns to its original 
height at the end of a year, by its course causing and 
marking the seasons. 

Nor is this all. The sun's motion is not merely north 
and south, but it also advances continually eastward among 
the stars, completing the circuit in a year. It is true that 
we cannot see the stars near the sun in the same way that 
we can those about the moon, so as to be able directly to 
perceive this motion; but in the spring the stars which are 
rising in the east at sunset are different from those which 
are found there in the summer or in the winter. In March 
the most conspicuous of the eastern constellations at 
sunset are Leo and Bootes. A little later Virgo appears ; 
in the summer Ophiuchus and Libra ; still later Scorpio ; 

1 Tlie student must carefully discriminate between "motion among 
the stars" and the diurnal motion, in which sun, moon, planets, and 
comets all partake along with the stars. 



90 LESSONS IN ASTRONOMY 

while in midwinter Orion and Taurus are ascending as the 
sun goes down. The combination of these two motions in 
declination and right ascension annually carries the sun 
around the heavens in the ecliptic (Sec. 20). 

So far as the obvious appearances are concerned, it is 
quite indifferent whether we suppose the earth to revolve 
around the sun, or vice versa. That the earth really moves, 
however, is absolutely demonstrated by two phenomena too 
minute and delicate for observation without the telescope, 
but accessible to modern methods. One of them is the 
aberration of light, the other the annual parallax of the 
fixed stars. These can be explained only by the actual 
motion of the earth, but we postpone their discussion for 
the present. (See Sec. 343, and Appendix, Sec. 435.) 

116. The Ecliptic; its Related Points and Circles. — By 
observing daily with the meridian circle the sun's declina- 
tion and the difference between its right ascension and 
that of some standard star, we obtain a series of positions 
of the sun's center which can be plotted on the globe, and 
we can thus mark out the path of the sun among the stars. 
It turns out to be a great circle, as is shown by its cutting 
the celestial equator at two points just 180° apart (the 
so-called " equinoctial points," or " equinoxes "), where it 
makes an angle with the equator of approximately 23i° 
(23° 27' 14" in 1890). 

This great circle, already several times referred to, is 
called the Ecliptic, because, as was early discovered, eclipses 
happen only when the moon is crossing it. Its position 
among the constellations is shown upon the equatorial star- 
maps. It may be defined as the circle in which the plane 
of the earth' s orbit cuts the celestial sphere. 



THE ECLIPTIC AXD THE ZODIAC 91 

The angle which the ecliptic makes with the equator at the equi- 
noctial points is called the Obliquity of the Ecliptic. This obliquit f is 
evidently equal to the sun's greatest distance from the equator, i.e., 
its maximum declination (23° 27'), which is reached in December 
and June. 

117. The two points in the ecliptic midway between the 
equinoxes are called the Solstices, because at these points 
the sun "stands," that is, ceases to move north or south. 
Two circles drawn through the solstices parallel to the 
equator are called the Tropics, or " turning-lines," because 
there the sun turns from its northward motion to the 
southward, or vice versa. The two points in the heavens 
90° distant from the ecliptic are called the Poles of the 
Ecliptic. The northern one is in the constellation of Draco, 
about midway between the stars Delta and Zeta Draconis, 
at a distance from the pole of the heavens equal to the 
obliquity of the ecliptic, and on the Solstitial Colure, the 
hour-circle which runs through the two solstices ; the hour- 
circle which passes through the equinoxes being called the 
Equinoctial Colure. Great circles drawn through the poles 
of the ecliptic, and therefore perpendicular, or " second- 
aries," to the ecliptic, are known as " circles of latitude." 
It will be remembered (Sec. 20) that celestial longitude and 
latitude are measured with reference to the ecliptic, and 
not to the equator. 

118. The Zodiac and its Signs. — A belt 16° wide (8° 
on each side of the ecliptic) is called the Zodiac, or zone 
of animals, the constellations in it, excepting Libra, being 
all figures of animals. It is taken of that particular 
width simply because the moon and all the principal 
planets always keep within it. It is divided into the 



92 LESSORS IN ASTRONOMY 

so-called signs, each 30° in length, having the following 
names and symbols : 

f Aries T f Libra £± 

Spring «{ Taurus y Autumn <[ Scorpio m 

1^ Gemini n ^Sagittarius f 

( Cancer ^b fCapricornus V? 

Summer ^ Leo Si Winter ^ Aquarius ~z 

^ Virgo t^ 1^ Pisces x 

The symbols are for the most part conventionalized pictures of 
the objects. The symbol for Aquarius is the Egyptian character for 
water. The origin of the signs for Leo, Capricornus, and Virgo is 
not quite clear. 

The zodiac is of extreme antiquity. In the zodiacs of 
the earliest history the Fishes, Ram, Bull, Lion, and 
Scorpion appear precisely as now. 

119. The Earth's Orbit. — The ecliptic must not be con- 
founded with the earth's orbit. It is simply a great circle 
of the infinite celestial sphere, — the trace made upon that 
sphere by the plane of the earth's orbit, which is its path 
in space. The fact that the ecliptic is a great circle gives 
us no information about the earth's orbit itself, except 
that it lies in a plane passing through the sun. It tells us 
nothing as to the orbit's real form and size. 

By reducing the observations of the sun's right ascension 
and declination through the year to longitude and latitude 
(the latitude would always be exactly zero except for some 
slight perturbations due chiefly to the moon's revolution 
around the earth), and combining these data with observa- 
tions of the sun's apparent diameter, we can, however, 
ascertain the form of the earth's orbit and the law <i£ its 



THE EARTH'S OKBIT 



93 



B 



motion. (The size of the earth's orbit, i.e., its scale of 
miles, cannot be fixed until we find the sun's distance.) 

The result is that the orbit is found to be very nearly a 
circle, but not exactly so. It is an oval or ellipse, with 
the sun at one of its foci (as illustrated in Fig. 13), but is 
much more nearly circular than the oval there represented. 
Its eccentricity is only about ^ ; that is to say, the dis- 
tance from the center of the sun to the middle of the 
ellipse is only about -^ of 
the average distance of the 
sun from the earth. 

The method by which 
we proceed to ascertain the A\ 
form of the orbit may be 
found in the Appendix, 
Sec. 428. (For a description 
of the ellipse, see Sec. 429.) 

120. Definition of Terms. 
— The points where the earth is nearest to and most 
remote from the sun are called respectively the Perihelion 
and the Aphelion (December 31 and June 30), the line 
joining them being the major axis of the orbit. This line, 
indefinitely produced in both directions, is called the 
Line of Apsides (pronounced Ap'si-deez), the major axis 
being a limited piece of it. A line drawn from the sun to 
the earth, or to any other planet at any point in its orbit, 
as SP in Fig. 13, is called the planet's Radius Vector. 

The variations in the sun's apparent diameter due to our 
changing distance are too small to be detected without a 
telescope, so that the ancients failed to perceive them. 
Hipparchus, however, about 120 B.C. discovered that the 



/^~~~7' 


\ 

\ 




^P 


/ / 








/ / 




\ 




/ / 




\ 




/ / ^ 




\ 












/ 7 ^""^ 






\ \ \ 


' /^-^ 






\ \ \ 


1 F C 


B' 




5 1 



Fig. 13. — The Ellipse 



94 



LESSORS IX ASTRONOMY 



earth is not in the center 1 of the circular orbit which he sup- 
posed the sun to describe around it with uniform velocity. 
Obviously the sun's apparent motion is not uniform, 
because it takes 186 days for the sun to pass from the 
vernal equinox, March 20, to the autumnal, September 22, 
and only 179 days to return. Hipparchus explained this 
on the hypothesis that the earth is out of the center of the 
circle. 

121. The Law of the Earth's Motion. — By combining 
the measured apparent diameter of the sun with the differ- 
ences of longitude from day 
to day we can deduce mathe- 
matically not only the form 
of the earth's orbit, but the 
law of her motion in it. It 
can be shown from the com- 
parison that the earth moves 
in such a way that its radius 
vector describes areas propor- 
tional to the time, a law which 
Kepler first brought to light in 1609 ; that is to say, if ah, 
cd, and ef (Fig. 14) be portions of the orbit described by the 
earth in different weeks, the areas of the elliptical sectors 
aSb, cSd, and eSf are all equal. A planet near perihelion 
moves faster than at aphelion in just such proportion as 
to preserve this relation. 

As Kepler left the matter, this is a mere fact of obser- 
vation. Newton afterwards proved that it is the necessary 




Fig. 14. — Equable Description of 
Areas 



1 Hipparchus (and every one else until the time of Kepler, 1007) 
assumed on metaphysical grounds that the sun's orbit must necessarily 
be a circle, and described with a uniform motion. 



CHANGES IN THE EARTH'S ORBIT 95 

mechanical consequence of the fact that the earth moves 
under the action of a force always directed towards the sun. 

It is true in every case of the elliptical motion of a heavenly 
body, and enables us to find the position of the earth or of any planet, 
when we once know the time of its orbital revolution (technically 
the " period ") and the time when it was last at perihelion. The 
solution of the problem, first worked out by Kepler, lies, however, 
quite beyond the scope of the present work. 

122. Changes in the Earth's Orbit. — The orbit of the 
earth changes slowly in form and position, though in the 
long run it is unchangeable as regards the length of its 
major axis and the duration of the year. 

These so-called " secular changes" are due to ''pertur- 
bations " caused by the action of the other planets upon 
the earth. Were it not for their attraction the earth would 
keep her orbit with reference to the sun and stars abso- 
lutely unaltered from age to age. 

Besides these secular perturbations of the earth's orbit, 
the earth itself is also continually being slightly disturbed 
in its orbit. On account of its connection with the moon 
it oscillates each month a few hundred miles above and 
below the true plane of the ecliptic, and by the action of 
the other planets is sometimes set backwards or forwards 
in its orbit to the extent of some thousands of miles. Of 
course every such displacement of the earth produces a 
corresponding slight change in the apparent position of 
the sun and of the nearer planets. 

123. The Seasons. — The earth in its motion around the 
sun always keeps its axis nearly parallel to itself during 
the whole year, for the mechanical reason that a spinning 
globe maintains the direction of its axis invariable, unless 



96 



LESSONS IX ASTRONOMY 



disturbed by some outside force (verj prettily illustrated 
by the gyroscope). Fig. 15 shows the way in which the 
north pole of the earth is tipped with reference to the sun 
at different seasons of the year. At the vernal equinox 
(March 20) the earth is situated so that the plane of its 
equator passes through the sun. At that time, therefore, 
the circle which bounds the illuminated portion of the 
earth passes through the two poles, as shown in Fig. 16, i>, 

Autumnal Equinox 



, 




Vernal Equinox 

Fig. 15. — The Seasons 

and day and night are therefore equal, as implied by the 
term "equinox." The same is again true on the '2'2d of 
September. About the 21st of June the earth is so situ- 
ated that its north pole is inclined towards the sun by 
about 23i°, as shown in Fig. 16, A, The south pole is 
then in the unlighted half of the earth's globe, while the 
north pole receives sunlight all day long, and in all por- 
tions of the northern hemisphere the day is longer than 



THE SKA SONS 



97 




the night. In the southern hemisphere, on the other hand, 
the reverse is true. 

At the time of the winter solstice the southern pole has 
perpetual sunshine, and the north pole is in the night. 

At the equator of the earth day and night are equal at 
all times of the year, and at that part of the earth there 
are no seasons in the proper sense of the word, though 
there are usually alternations of rain and drought due to 
changes in the direction of the winds. Everywhere else 
the day and night are unequal, 
except when the sun is at one 
of the equinoxes. 

In high latitudes the inequal- 
ity between the lengths of the 
day in summer and in winter 
is very great; and at places 
within the polar circle there 
are always days in winter when the sun does not rise at 
all, and others in the summer when it does not set, but 
exhibits the phenomenon of the "midnight sun," as 
already explained in Sec. 86. At the pole itself the 
summer is one perpetual day, six months in length, while 
the winter is a six-months night. 

Perhaps the student will get a better idea by thinking of the earth 
as a globe floating, just half immersed, on a sheet of still water, and 
so weighted that its poles dip at an angle of 23J°, while it swims in 
a circle around the sun, a much larger globe, also floating on the 
same surface. The sheet of water corresponds to the ecliptic, while 
the plane of the equator is a circle on the globe itself, drawn square 
to the axis. If now the axis is kept pointing always the same way 
(always north, for instance), while the globe swims around, things 
will correspond to the motion of the earth around the sun. 



Fig. 1(5. —Position of Pole at 
Solstice and Equinox 



98 LESSONS IN ASTRONOMY 

124. Effects on Temperature. — The changes in the dura- 
tion of insolation (exposure to sunshine) at any place involve 
changes of temperature, thus producing the seasons. It is 
clear that the surface of the soil at any place in the north- 
ern hemisphere will receive daily from the sun more than 
the average amount of heat whenever he is north of the 
celestial equator, and for two reasons : 

1. Sunshine lasts more than half the day. 

2. The mean altitude of the sun during the day is greater 
than the daily average for the year, since he is higher at 

noon than at the time of the 

// V^X equinox, and in any case 

v/y^// ^^\?\ reac h es the horizon at rising 

y/^iS /'^ and setthig. 

// ygT \ x y' yS Now the more obliquely 

~~/\ nTT^/^ the rays strike, the less heat 

tf— — ! -^ they bring to each square 

Fig. 17. -Effect of Sun's Elevation inch of surface, as is obvious 
on Amount of Heat imparted to from Fig. 17. A beam of SU11- 

shine which would cover the 
surface AC, if received squarely, will be spread over a 
much larger surface, Ac, if it falls at the angle h. The 
difference in favor of vertical rays is further exaggerated 
by the absorption of heat in our atmosphere, because the 
rays that are nearly horizontal have to traverse a much 
greater thickness of air before reaching the ground. 

For these two reasons, therefore, the temperature rises 
rapidly for a place in the northern hemisphere as the sun 
comes north of the equator. We, of course, receive the 
most heat in twenty-four hours at the time of the summer 
solstice ; but this is not the hottest time of the summer. 



PRECESSION 99 

The weather is then getting hotter, and the maximum 
will not be reached until the increase ceases, Le., not 
until the amount of heat lost in twenty-four hours equals 
that received in the same time. This maximum is reached 
in our latitude about the 1st of August. For similar 
reasons the minimum temperature in winter occurs about 
February 1. 

125. Precession of the Equinoxes. — This is a slow west- 
ward motion of the equinoxes along the ecliptic. In explain- 
ing the seasons we have said (Sec. 123) that the earth keeps 
its axis nearly parallel to itself during its annual revolu- 
tion. It does not maintain strict parallelism, however ; but 
owing to the attraction of the sun and moon on that portion 
of the mass of the earth which projects, like an equatorial 
ring, beyond the true spherical surface, the earth's axis 
continually but slowly shifts its place, keeping always 
nearly the same inclination to the plane of the ecliptic, so 
that its pole revolves in a small circle of 23i° radius around 
the pole of the ecliptic once in 25,800 years. Of course 
the celestial equator must move also, since it has to keep 
everywhere just 90° from the celestial pole ; and, as a 
consequence, the equinoxes move westward on the ecliptic 
about 50^.2 each year, as if to meet the sun. This motion 
of the equinox was called " precession" by Hipparchus, who 
discovered 1 it about 125 B.C., but could not explain it. 
The explanation was not reached until the time of Newton, 
about 20 Q years ago, who showed it to be a necessary result 
of gravitation operating under the actual conditions. 

1 He discovered it by finding that in his time the place of the equinox 
among the stars was no longer the same that it used to be in the days of 
Homer and Hesiod, several hundred years before. 



100 LESSONS IN ASTRONOMY 

126. Effect of Precession upon the Pole and the Zodiac. — 
At present the Pole-star, Alpha Ursse Minoris, is about 
li° from the pole, while in the time of Hipparchus the 
distance was fully 12°. During the next two centuries 
the distance will diminish to about 30', and then begin to 
increase. 

If upon the celestial globe we trace a circle of 23^° 
radius around the pole of the ecliptic as a center, it will 
mark very nearly the track of the celestial pole among 
the stars. 

Other causes slightly shift the position of the ecliptic and its pole, 
so that the actual path of the pole among the stars deviates sensibly 
from an exact circle. 

It passes not very far from Alpha Lyrse (Vega), on the opposite 
side of the circle from the present Pole-star ; about 12,000 years hence 
Vega will, therefore, be the Pole-star. Reckoning backwards, we 
find that some 4000 years ago Alpha Draconis (Thuban) was the 
Pole-star, and about 3^° from the pole. 

Another effect of precession is that the signs of the 
zodiac do not now agree with the constellations which 
bear the same name. The sign of Aries is now in the 
constellation of Pisces, and so on, each sign having 
"backed" bodily, so to speak, into the constellation west 
of it. 

The forces which cause precession do not act quite uni- 
formly, and as a result the rapidity of the precession varies 
somewhat, and there is also a slight tipping or nodding of 
the earth's axis, which is called nutation, (For a fuller 
account of the whole matter, see General Astronomy, 
Arts. 209-215.) 



EARTH'S ORBITAL MOTION 101 

THE YEAR AND THE CALENDAR 

127. Three different kinds of "year" are now recog- 
nized, — the Sidereal, the Tropical (or Equinoctial), and 
the Anomalistic. 

The sidereal year, as its name implies, is the time 
occupied by the sun hi apparently completing the circuit 
from a given star to the same star again. Its length is 
365 d 6 b 9 m 9 s . From the mechanical point of view this is 
the true year, i.e., it is the time occupied by the earth in 
completing its revolution around the sun from a given 
direction in space to the same direction again. 

The tropical year is the time included between two suc- 
cessive passages of the vernal equinox by the sun. Since 
the equinox moves yearly 50". 2 towards the west, the trop- 
ical year is shorter than the sidereal by about twenty minutes, 
its length being SGo^MS 11 ^ 8 . Since the seasons depend 
on the sun's place with respect to the equinox, the tropical 
year is the year of chronology and civil reckoning. 

The third kind of year is the anomalistic year, — the time between 
two successive passages of the perihelion by the earth. Since the 
line of apsides of the earth's orbit makes an eastward revolution once 
in about 108,000 years, this kind of year is nearly five minutes longer 
than the sidereal, its length being Sed^loMS 8 . It is but little used 
except in calculations relating to perturbations of the planets. 

128. The Calendar. — The natural units of time are the 
day, the month, and the year. The day is too short for 
convenience in dealing with considerable periods, such as 
the life of a man, for instance ; and the same is true even 
of the month; so that for all chronological purposes the 
tropical year (the year of the seasons) has always been 



102 LESSONS IN ASTRONOMY 



employed. At the same time, so many religious ideas and 
observations have been connected with the changes of the 
moon that there has been a constant struggle to reconcile 
the month with the year. Since the two are incommen- 
surable, no really satisfactory solution is possible, and the 
modern calendar of civilized nations entirely disregards the 
lunar phases. In early times the calendar was in the hands 
of the priesthood and was mainly lunar, the seasons being 
either disregarded or kept roughly in place by the occa- 
sional putting in or dropping of a month. The Moham- 
medans still use a purely lunar calendar, having a " year " 
of twelve months, which contains alternately 354 and 355 
days. In their reckoning the seasons fall continually in 
different months, and their calendar gains on ours about 
one year in thirty-three. 

129. The Julian Calendar. — When Julius Caesar came 
into power he found the Roman calendar in a state of 
hopeless confusion. He, therefore, with the advice of 
Sosigenes, the astronomer, established (45 B.C.) what is 
known as the Julian calendar, which still, either untouched 
or with a trifling modification, continues in use among civil- 
ized nations. Sosigenes discarded all reference to the 
moon's phases, and adopting 365i days as the true 
length of the year, he ordained that every fourth year 
should contain 366 days, — the extra day being inserted 
by repeating the sixth day before the Calends of March 
(whence such a year is called " Bissextile "). He also 
transferred the beginning of the year, which before Caesar's 
time had been in March (as is indicated by the names of 
several of the months, — December, the tenth month, for 
instance), to January 1. 



a 



THE CALENDAR 103 

C?esar also took possession of the month Quintilis, naming it 
July after himself. His successor, Augustus, in a similar marffter 
appropriated the next month, Sextilis, calling it August, and to vin- 
dicate his dignity and make his month as long as his predecessor's 
he added to it a day stolen from February. 

The Julian calendar is still used unmodified in the 
Greek Church, and also in many astronomical reckonings. 

130, The Gregorian Calendar. — The true length of the 
tropical year is not 365i days, but 365 d 5 h 48 m 46 s , leaving 
a difference of ll m 14 s by which the Julian year is too 
long. This difference amounts to a little more than three 
days in 400 years. As a consequence the date of the 
vernal equinox comes continually earlier and earlier in 
the Julian calendar, and in 1582 it had fallen back to 
the 11th of March instead of occurring on the 21st as it 
did at the time of the Council of Nice (A.D. 325). 

Pope Gregory, therefore, under the astronomical advice 
of Clavius, ordered that the calendar should be restored by 
adding ten days, so that the day following Oct. 4, 1582, 
should be called the 15th instead of the 5th ; further, to 
prevent any future displacement of the equinox, he decreed 
that thereafter only such century years should be leap years 
as are divisible by 400. Thus, 1700, 1800, 1900, and 2100 
are not leap years, but 1600 and 2000 are. 

The change was immediately adopted by all Catholic 
countries, but the Greek Church and most Protestant 
nations refused to recognize the pope's authority. The new 
calendar was, however, at last adopted in England in 1752, 
so that now the " old style " is used only in Russia and 
Greece, and a few other minor nations of eastern Europe. 
At present (since the years 1800 and 1900 were leap years 



104 LESSONS m ASTRONOMY 

in the Julian calendar and not in the Gregorian) the differ- 
ence between the two calendars is thirteen days. 

In 1900 there was a good deal of discussion about 
the beginning of the twentieth century. According to the 
accepted chronological method of reckoning, the begin- 
ning of the Christian era is reckoned from the beginning 
of the year A.d. 1, the year preceding being 1 B.C., with 
no intervening year "zero." It follows that the first 
century was not completed until the end of the year 
A.D. 100, and that the second century began with A.D. 101, 
as the twentieth did with the year 1901. 

Certain chronologers about two hundred years ago tried 
to reform the method of reckoning by inserting a year 
A.D. as the beginning of the Christian era, and the plan 
would offer some slight advantages. It did not, however, 
meet with any general acceptance, though it was for a time 
adopted in a few astronomical books and tables. 



CHAPTER V 

THE MOON 

Her Orbital Motion and the Month — Distance, Dimensions, Mass, Density, 
and Force of Gravity — Rotation and Librations — Phases — Light and 
Heat — Physical Condition — Telescopic Aspect and Peculiarities of the 
Lunar Surface 

131. Next to the sun, the moon is the most conspicuous 
and to us the most important, of the heavenly bodies ; in 
fact, she is the only one except the sun which exerts the 
slightest perceptible influence upon the interests of human 
life. She owes her conspicuousness and her importance, 
however, solely to her nearness; for she is really a very 
insignificant body as compared with stars and planets. 

132. The Moon's Apparent Motion ; Definition of Terms, 
etc. — One of the earliest observed of astronomical phe- 
nomena must have been the eastward motion of the moon 
with reference to the sun and stars, and the accompany- 
ing change of phase. If, for instance, we note the moon 
to-night as very near some conspicuous star, we shall find 
her to-morrow night at a point considerably farther east, 
and the next night farther yet; she changes her place 
about 13° daily, and makes the complete circuit of the 
heavens, from star to star again, in about 27 J days. In 
other words, she revolves around the earth in that time, 
while she accompanies us in our annual journey around 
the sun. Since the moon moves eastward among the stars 
so much faster than the sun (which takes a year in going 

105 



106 LESSONS IN ASTRONOMY 

once around), she overtakes and passes him at regular 
intervals ; and as her phases depend upon her apparent 
position with reference to the sun, this interval from new 
moon to new moon is specially noticeable, and is what we 
ordinarily understand as the " month." 

The angular distance of the moon east or west of the sun 
at any time is called her Elongation. At new moon it is zero, 
and the moon is said to be in Conjunction. At full moon 
the elongation is 180°, and she is said to be in Opposition. 
In either case the moon is in Syzygy. [Syzygy means " yoked 
together," thesun, moon, and earth being then nearly inline.) 
When the elongation is 90° she is said to be in Quadrature. 

133. Sidereal and Synodic Months. — The sidereal month 
is the time it takes the moon to make her revolution from 
a given star to the same star again; its length is 27 J days 
(27 d 7 h 43 m ll s .524). The mean daily motion, therefore, is 
360° divided by this, or 13° 11' (nearly). The sidereal 
month is the true month from the mechanical point of 
view. On account of " perturbations," it varies in length 
by as much as three hours from time to time. 

The synodic month is the time between two successive 
conjunctions or oppositions ; i.e., between two successive 
new or full moons. Its average length is about 29i days 
(29 d 12 h 44 m 2 s .841), but it varies nearly thirteen hours, 
mainly on account of the eccentricity of the moon's orbit. 

If M be the mean length of the moon's sidereal period in days, 
E the length of the sidereal year, and S the mean length of the 
synodic month, the three quantities are connected by a simple relation 

easily demonstrated. — is the fraction of a circumference moved 
J M 

over by the moon in a day. Similarly, — is the apparent daily motion 



THE MOOD'S PATH 107 

of the sun. The difference is the amount which the moon gains on 
the sun daily. Xow it gains a whole revolution in one synodic 

month of S days, and therefore must gain daily — of a circum- 

o 

ference. Hence we have the important equation 

1 _ 1 1 
M E~~S' 

which is known as the equation of synodic motion. In a sidereal 
year the number of sidereal months is exactly one greater than the 
number of synodic months, the numbers being respectively 13.369 -f 
and 12.369 +. 

134. The Moon's Path among the Stars. — By observing 
the moon's right ascension and declination daily with 
suitable instruments Ave can map out its apparent path, 
just as in the case of the sun (Sec. 116). This path turns 
out to be (very nearly) a great circle, inclined to the eclip- 
tic at a slightly variable angle of about 5° 8'. The two 
points where it cuts the ecliptic are called the " nodes," 
the ascending node being where the moon passes from the 
south side to the north side of the ecliptic, while the 
opposite node is called the descending node. 

The moon at the end of the month never comes back exactly to 
the point of beginning among the stars, on account of the so-called 
" perturbations " of her orbit, due mostly to the attraction of the 
sun. One of the most important of these perturbations is the 
" regression of the nodes. " These slide westward on the ecliptic just 
as the vernal equinox does (precession), but much faster, completing 
their circuit in about nineteen years instead of 26,000. 

135. Interval between the Moon's Successive Transits ; 
Daily Retardation. — Owing to the eastward motion of 
the moon among the stars it comes to the meridian about 
51 minutes later each day, on the average ; but the 



108 LESSONS m ASTRONOMY 

retardation ranges all the way from 38 minutes to 66 
minutes, on account of the variation in the rate of the 
moon's motion. 

The average retardation of the moon's rising and setting 
is also the same 51 minutes ; but the actual retardation 
is still more variable than that of the meridian transits, 
depending to some extent on the latitude of the observer 
as well as on the variations in the moon's motion. 

At New York the range is from 23 minutes to l h 17 m ; 
that is to say, on some nights the rising of the moon is 
only 23 minutes later than on the preceding night, while 
at other times it is more than an hour and a quarter behind- 
hand. In high latitudes the differences are still greater. 
In very high latitudes the moon, when it has its greatest 
possible declination, becomes circumpolar for a certain time 
each month, and remains visible without setting at all 
(like the midnight sun) for a greater or less number of 
days, according to the latitude of the observer. 

There is always one day in the month on which the moon does 
not rise, and another on which it does not set. Why ? 

136. Harvest and Hunter's Moon. — The full moon that 
occurs nearest the autumnal equinox is called the " harvest 
moon "; the one next following, the " hunter's moon." At 
that time of the year the moon, while nearly full, rises for 
several consecutive nights almost at the same hour, so that 
the moonlight evenings last for an unusually long time. 
The phenomenon, however, is much more striking in north- 
ern Europe and in Canada than in the United States. 

137. Form of the Moon's Orbit. — By observation of the 
moon's apparent diameter in connection with observations 



FORM OF MOON'S ORBIT 109 

of her place in the sky, we can determine the form of her 
orbit around the earth in the same way that the form of 
the earth's orbit around the sun was worked out. (See 
Appendix. Sec. -428.) The moon's apparent diameter ranges 
from 33' 33". when as near the earth as possible, to 29' 24", 
when most remote : and her orbit turns out to be an ellipse 
like that of the earth around the sun. but of much greater 
eccentricity, averaging about r V (as against J^). We say 
" averaeine " because the actual eccentricity is variable on 
account of perturbations. 

The point of the moon's orbit nearest the earth is called 
the Perigee, that most remote the Apogee, and the indefi- 
nite line passing through these points the Line of Apsides, 
while the major axis is that portion of this line which lies 
between the perigee and apogee. This line of apsides is 
in continual motion on account of perturbations (just as 
the line of nodes is. Sec. 13-4), but it moves eastward instead 
of westward, completing its revolution in about nine years. 

In her revolution about the earth the moon observes the 
same law of equal areas that the earth does hi her orbit 
around the sun (Sec. 121). 



THE MOOX'S DISTAXCE 






138. In the case of any heavenly body, one of the first 
and most fundamental inquiries relates to its distance from 
us ; until the distance has been measured we can get no 
knowledge of the real dimensions of its orbit, nor of the 
size, mass, etc., of the body itself. The problem is usually 
solved by measuring the apparent " parallactic " displace- 
ment of the moon as seen by observers at widely separated 



110 LESSONS IN ASTRONOMY 

stations. Before proceeding farther we must, therefore, 
say a few words upon the subject of parallax. 

139. Parallax. — In general, the word " parallax " means 
the difference between the directions of a heavenly body 
as seen by the observer and as seen from some standard 
point of reference. The annual or heliocentric parallax of 
a star is the difference of the star's direction as seen from 
the earth and from the sun. The diurnal or geocentric 
parallax of the sun, the moon, or a planet is the difference 
between its direction as seen from the center of the earth 
and from the observer's station on the earth's surface ; or, 
what comes to the same thing, the geocentric parallax is the 
angle at the body made by two lines drawn from it, one to 
the observer, the other to the center of the earth. (Stars have 
no sensible geocentric parallax; the earth as seen from 
them is a mere point.) 

In Fig. 18 the parallax of the body P, for an observer 
at 0, is the angle OPC. Obviously this diurnal parallax 
is zero for a body directly overhead at Z, and is the greatest 
possible for a body on the horizon, as at P h . 

Moreover, and this is to be specially noted, this parallax 
of a body at the horizon — the " horizontal parallax " — is 
simply the angular semi-diameter of the earth as seen from 
the body. When, for instance, we say that the moon's hori- 
zontal parallax is 57', it is equivalent to saying that seen 
from the moon the earth appears to have a diameter of 114'. 
In the same way, since the sun's parallax is 8". 8, the 
diameter of the earth as seen from the sun is 17". 6. 

140. Relation between Parallax and Distance When 

the horizontal parallax of any heavenly body is ascertained 
its distance follows at once through our knowledge of the 






PARALLAX 



111 



earth's dimensions. If we know how large a ball of given 
size appears, we can tell how far away it is ; if we know 
how large the earth looks from the moon, we can find the 
distance between them. Thus, when in the triangle CP h O 
(Fig. 18) we know the angle at P h , and the side CO, the 
radius of the earth, we can compute CP h by a very easy 
trigonometrical calculation. Evidently the more remote 
the body, the smaller its 
parallax. 

Since the radius of the 
earth varies slightly in dif- 
ferent latitudes, we take the 
equatorial radius as a stand- 
ard, and the equatorial hori- 
zontal parallax is the earth's 
equatorial semi-diameter as 
seen from the body. It is 
this which is usually meant 
when we speak simply of 
"the parallax" of the moon, of the sun, or of a planet 
without adding any qualification, but never when we speak 
of the parallax of a star; then we always mean the annual 
parallax. 

141. Parallax, Distance, and Velocity of the Moon. — 
The moon's equatorial horizontal parallax found by corre- 
sponding observations made at different parts of the earth is 
3422" (oT' 2") according to Xeison, but varies considerably 
on account of the eccentricity of the orbit. From this paral- 
lax we find that the moon's average distance from the earth 
is about 60.3 times the earth's equatorial radius, or 238,840 
miles, with an uncertainty of perhaps twenty miles. 




Diurnal Parallax 



112 LESSONS IN ASTRONOMY 

The maximum and minimum values of the moon's distance are 
given by Neison as 252,972 and 221,617 miles. It will be noted that 
the average distance is not the mean of the two extremes. 

Knowing the size and form of the moon's orbit, the 
velocity of her motion is easily computed. It averages a 
little less than 2300 miles an hour, or about 3350 feet per 
second. Her mean apparent angular velocity among the 
stars is about 33', which is just a little greater than the 
apparent diameter of the moon itself. 

142. Diameter, Area, and Bulk of the Moon. — The mean 
apparent diameter of the moon is SV 7". Knowing its 
distance, its real diameter comes out 2163 miles. This 
is 0.273 of the earth's diameter. 

Since the surfaces of globes vary as the squares of their 
diameters, and their volumes as the cubes, this makes 
the surface area of the moon equal to about ^ of the 
earth's, and the volume (or bulk) almost exactly ^ of 
the earth's. 

No other satellite is nearly as large as the moon in comparison 
with its primary planet. The earth and moon together, as seen from 
a distance, are really in many respects more like a double planet than 
like a planet and satellite of ordinary proportions. At a time, for 
instance, when Venus happens to be nearest the earth (at a distance 
of about 25,000000 miles) her inhabitants (if she has any) would 
see the earth just about as brilliant as Venus herself at her best 
appears to us, and the moon would be about as bright as Sirius, 
oscillating backwards and forwards about J° each side of the earth, 
once a month. 

143. Mass, Density, and Superficial Gravity of the Moon. 
— Her mass is about -gL- of the earth's mass (0.0125). The 
actual measurement of the moon's mass is an extremely 






THE MOON'S ROTATION 113 

difficult problem, and the methods pursued are quite beyond 

the scope of this book. Since the density is equal to ^7— = , 

the density of the moon as compared to that of the earth 
is found to be 0.613, or about 3.4 the density of water 
(the earth's density being 5.58). This is a little above 
the average density of the rocks which compose the crust 
of the earth. 

The " superficial gravity," or the attraction of the moon 
for bodies at its surface, is only about one-sixth that at the 
surface of the earth. This is a fact that 
must be borne in mind in connection XL 
with the enormous scale of the craters on 
the moon. Volcanic forces there would 
throw materials to a vastly greater dis- 
tance than on the earth. 

144. Rotation of the Moon. — The 
moon turns on its axis once a month, in 
exactly the time occupied by its revo- 



tr 



Fig. 19 
lution around the earth; its day and 

night are, therefore, each nearly a fortnight in length, and 
in the long run it keeps the same side always toward the 
earth. We see to-day precisely the same face of the moon 
which Galileo did when he first looked at it with his tele- 
scope. The opposite face has never been seen from the 
earth, and probably never will be. 

It is difficult for some to see why a motion of this sort should 
be considered a rotation of the moon, since it closely resembles the 
motion of a ball carried on a revolving crank (Fig. 19). Such a 
hall, they say, " revolves around the shaft, but does not rotate on its 
own axis." It does rotate, however ; for if we mark one side of the 



114 LESSONS W ASTRONOMY 

ball, we shall find the marked side presented successively to every 
point of the compass as the crank turns around, so that the ball 
turns on its own axis as really as if it were whirling upon a pin 
fastened to the table. By virtue of its connection with the crank, 
the ball has two distinct motions: (1) the motion of translation, 
which carries its center in a circle around the shaft ; (2) an addi- 
tional motion of rotation around a line drawn through its center of 
gravity parallel to the shaft. 

Rotation consists essentially in this : A line connecting any two 
points in the rotating body, and produced to the celestial sphere, will 
sweep out a circle upon it. In every rotating body one line, however, 
can be drawn through the center of the body, so that the circle 
described by it in the sky will be infinitely small. This is the axis 
of the body. 

145. Librations. — The behavior of the moon, however, differs 
essentially from that of the ball on the crank, showing that her rota- 
tion and orbital revolution are really independent., though identical 
in period. While in the long run the moon keeps the same face 
towards the earth, it is not so from day to day. With reference to 
the center of the earth, it is continually oscillating a little, and 
these oscillations constitute what are called Librations, of which we 
distinguish three: (1) the libration in latitude, by which the north 
and south poles are alternately presented to the earth; (2) the 
libration in longitude, by which the east and west sides of the moon 
are alternately tipped a little towards us ; and (3) the diurnal libra- 
tion, which enables us to look over whatever edge of the moon is 
uppermost when it is near the horizon. Owing to these librations, 
we see considerably more than half of the moon's surface at one time 
and another. About 41 per cent of it is always visible ; 41 per cent 
never visible ; and a belt at the edge of the moon, covering about 
18 per cent, is rendered alternately visible and invisible by libration. 
The explanation of the peculiarity of the moon's rotation is to be 
found in the theory of " tidal evolution." (See Manual of Astronomy, 
Sec. 346.) 

146. Phases of the Moon. — Since the moon is an opaque 
globe shining merely by reflected light, we can see only 



THE MOON'S PHASES 



115 



that hemisphere of her surface on which the sun is shining, 
and of the illuminated hemisphere only that portion which 
happens to be turned towards the earth. 

When the moon is between the earth and the sun (new 
moon) the side presented to us is dark, and the moon is 




Fig. 20. — The Moon's Phases 



then invisible. A week later, at the end of the first quarter, 
half of the illuminated hemisphere is visible, and we have 
the half-moon, as we also do a week after the full. Between 
the new moon and the half-moon, during the first and last 



116 LESSONS IN ASTRONOMY 

quarters of the lunation, we see less than half of the 
illuminated portion, and then have the " crescent " phase. 
Between half-moon and the full moon, during the second 
and third quarters of the lunation, we see more than half 
of the moon's illuminated side, and we have then what is 
called the " gibbous " phase. 

Fig. 20 (in which the light is supposed to come from a point far 
above the circle which represents the moon's orbit) shows the way in 
which the phases are distributed through the month. 

The line which separates the dark portion of the disk 
from the bright is called the Terminator, and is always a 
semi-ellipse, since it is a semicircle viewed obliquely, as 
shown by Fig. 21, A, Draftsmen sometimes incorrectly 
represent the crescent form by a construction like Fig. 21, B, 

in which a smaller circle has a por- 
tion cut out of it by an arc of a 
larger one. It is to be noticed also 
that ab, the line which joins the 
"cusps," or points, of the crescent, 
is always perpendicular to a line 
drawn from the moon to the sun, so 
that the horns are always turned directly away from the sun. 
The precise position in which they will stand at any time 
is, therefore, perfectly predictable and has nothing whatever 
to do with the weather. (Pupils have probably heard of 
the "wet moon" and "dry moon" superstition.) 

147. Earth-Shine on the Moon Near the time of new 

moon the portion of the moon's disk which does not get 
the sunlight is easily visible, illuminated by a pale reddish 
light. This light is earth-shine, — the earth as seen from 
the moon being then nearly " full." The red color is due to 




THE MOON'S PHYSICAL CHARACTERISTICS 117 

the fact that the light sent to the moon from the earth has 
passed twice through our atmosphere, and so has acquired 
the sunset tinge. Seen from the moon, the earth would 
be itself a magnificent moon about 2° in diameter, showing 
the same phases as the moon does to us. 

Taking everything into account, the earth-shine is probably fifteen 
to twenty times as strong as the light of the moon at similar phases. 
Since the moon keeps always the same face towards the earth, the 
earth is visible only from that part of the moon w T hich faces ns, and 
remains nearly stationary in the lunar sky, neither rising nor setting. 
It is easy to see that she would be a very beautiful object, on account 
of the changes which would be continually going on upon her surface 
due to snow, storms, clouds, growth of vegetation, etc. 

PHYSICAL CHARACTERISTICS OF THE MOO^ 

148. Absence of Air and Water. — The moon's atmos- 
phere, if there is any, is extremely rare, its density at the 
moon's surface being probably not more than j-^-q-q part of 
that of our own atmosphere. 

The evidence on the point is twofold : First, the telescopic appear- 
ance. There is no haze, shadows are perfectly black; there is no 
sensible twilight at the points of the crescent, and all outlines are 
visible sharply and without the least blurring such as would be due 
to the intervention of an atmosphere. Second, the absence of refrac- 
tion when the moon intervenes between us and any distant body. 
When the moon " occults " a star, for instance, there is no distortion 
or discoloration of the star -disk, but both the disappearance and the 
reappearance are practically instantaneous. 

Of course if there is no air, there can be no liquid water, 
since the water would immediately evaporate and form an 
atmosphere of vapor if air were not present. It is not impos- 
sible, however, nor perhaps improbable, that solid water (ice 



118 LESSONS IX ASTRONOMY 

and snow) may exist on the moon's surface. Although ice 
and snow liberate a certain amount of vapor, yet at a low 
temperature the quantity would be insufficient to make an 
atmosphere dense enough to be observed from the earth. 

If the moon once formed a portion of the earth, as is likely, the 
absence of air and water requires explanation, and there have been 
many interesting speculations on the subject into which we cannot 
enter. (The student is referred to the Manual of Astronomy, 
Sec. 209.) 

149. The Moon's Light. — In its quality moonlight is 
simply sunlight, showing a spectrum identical in every 
detail with that of the light coming from the sun itself, 
except as the intensity of different portions of the spectrum 
is slightly altered by its reflection from the lunar surface. 

The brightness of full moonlight as compared with sun- 
light is about one six-hundred-thousandth. According to 
this, if the whole visible hemisphere were packed with full 
moons, we should receive from it only about one-eighth of 
the light of the sun. 

The half-moon does not give nearly half as much light 
as the full moon. Near the full the brightness is suddenly 
and greatly increased, probably because at any time except 
the full the moon's visible surface is more or less darkened 
by shadows which disappear at the moment of full. 

The average " albedo," or reflecting power, of the moon's 
surface is given by Zollner as 0.174 ; i.e., the moon's sur- 
face reflects a little more than one-sixth of the light that 
falls upon it. There are, however, great differences in the 
brightness of the different portions of the moon's surface. 
Some spots are nearly as white as snow or salt, and others 
as dark as slate. 



THE MOON'S HEAT 119 

150. Heat of the Moon For a long time it was impos- 
sible to detect the moon's heat by observation. Even when 
concentrated by a large lens, it is too feeble to be shown 
by the most delicate thermometer. With modern appa- 
ratus, however, it is easy enough to perceive the heat of 
lunar radiation, though the measurement is extremely diffi- 
cult. The total amount of heat sent by the full moon to 
the earth appears to be about -jy-^oo o" °^ ^at sen ^ ^y ^he 
sun ; i.e., the full moon in two days sends us about as much 
heat as the sun does in one second. But the results of 
different observers differ rather widely. 

A considerable portion of the lunar heat seems to be 
simply reflected from the surface like light, while the rest, 
perhaps three-fourths of the whole, is " obscure heat," i.e., 
heat which has first been absorbed by the moon's surface 
and then radiated, like the heat from a brick that has been 
warmed by the sunshine. 

As to the temperature of the moon's surface, it is impos- 
sible to be very certain. During the long lunar night of 
fourteen days the temperature must inevitably fall appall- 
ingly low, — perhaps 200° or 300° below zero. On the 
other hand, the lunar rocks are exposed to the sun's rays 
in a cloudless sky for fourteen days at a time, so that if 
they were protected by air, like the rocks upon the earth, 
they would certainly become intensely heated. The obser- 
vations of Very in 1899, the latest and apparently conclu- 
sive, seem to show that on all the dark portion of the moon, 
and near its boundary on the illuminated portion even, the 
temperature is far below zero, and may fall as low as that 
of liquid air ; but that in the equatorial regions the temper- 
ature a few hours after " noon " rises very high, probably 



120 LESSONS m ASTRONOMY 

above that of boiling water, thus confirming Lord Rosse's 
conclusion of more than thirty years ago. But the mean 
temperature of even the equatorial regions is probably 
everywhere below the freezing point of water. 

151. Lunar Influences on the Earth. — The most impor- 
tant effect produced upon the earth by the moon is the 
generation of the tides in cooperation with the sun. There 
are also certain well-ascertained disturbances of the terres- 
trial magnetism connected with the approach and recession 
of the moon in its oval orbit ; and this ends the chapter of 
proved lunar influences. 

The multitude of current beliefs as to the controlling 
influence of the moon's phases and changes upon the weather 
and the various conditions of life are mostly unfounded. 
It is quite certain that if the moon has any influence at all 
of the sort imagined, it is extremely slight, — so slight that 
it has not yet been demonstrated, though numerous inves- 
tigations have been made expressly for the purpose of 
detecting it. Different workers continually come to con- 
tradictory results. 

152. The Moon's Telescopic Appearance. — Even to the 
naked eye the moon is a beautiful object, diversified with 
curious markings connected with numerous popular legends. 
In a powerful telescope these naked-eye markings vanish, 
and are replaced by a multitude of smaller details which 
make the moon, on the whole, the most interesting of all 
telescopic objects — especially to instruments of moderate 
size, say from six to ten inches in diameter, which gener- 
ally give a more pleasing view than instruments either 
much larger or much smaller. An instrument of this size, 
with magnifying powers between 250 and 500, virtually 



THE MOON'S SURFACE STRUCTURE 



121 



brings the moon within a distance ranging from 1000 to 
500 miles. Any object half a mile in diameter on the 
moon is distinctly visible. A long line or streak even less 
than a quarter of a mile across can easily be seen. 

For most purposes the best time to look at the moon is when it is 
between six and ten days old ; at the time of full moon few parts of the 
surface are well seen. It is evident that while with the telescope we 
should be able to see such objects as lakes, rivers, forests, and great cit- 
ies, if they existed on the moon, it would be hopeless to expect to distin- 
guish any of the minor indications of life, such as buildings or roads. 

I 153. The Moon's Surface Structure. — The moon's sur- 
face for the most part is extremely broken. The earth's 
mountains are 
mainly in long 
ranges, like the 
Andes and Hima- 
layas. On the 
moon the ranges 
are few in num- 
ber; but, on the 
other hand, the 
surface is pitted 
all over with great 
craters, which 
resemble very 

closely the volcanic craters on the earth's surface, though 
on an immensely greater scale. The largest terrestrial 
craters do not exceed six or seven miles in diameter ; many 
of those on the moon are fifty or sixty miles across, and 
some more than a hundred, while scores are from five to 
twenty miles in diameter. 




Fig. 22. — Normal Lunar Crater 



122 



LESSONS IN ASTRONOMY 



The normal lunar crater (Fig. 22) is nearly circular, sur- 
rounded by a mountain ring, which rises anywhere from 
1000 to 20,000 feet above the neighboring country. The 
floor within the ring may be either above or below the out- 
side level ; some craters are deep, and some are filled 
nearly to the brim. Frequently in the center of the 
crater there rises a group of peaks which attain the same 

elevation as the 
encircling ring, and 
these central peaks 
often show holes or 
minute craters in 
their summits. 

On some portions 
of the moon these 
craters stand very 
thickly. This is es- 
pecially the case near 
the moon's south 
pole. It is noticeable, 
also, that as on the 
earth the youngest 
mountains are gen- 
erally the highest, so 
on the moon the most 
recent craters are generally deepest and most precipitous. 
The height of a lunar mountain can be measured with 
notable accuracy by means of its shadow. 

The striking resemblance of these lunar craters to terrestrial 
volcanoes makes it natural to assume that they have a similar 
origin. This, however, is not quite certain, for there are notable 




Fig. 23. — Gassendi 



LUNAR FORMATIONS 



123 



difficulties in the way of the volcanic theory, especially in the case of 
what are called the great "Bulwark Plains," so extensive that a 
person standing in the center could not even see the summit of the 
surrounding ring at any point ; and yet there is no line of distinction 
between them and the smaller craters, — the series is continuous. 
Moreover, on the earth volcanoes necessarily require the action of 
air and water, which do not now exist on the moon ; so that if these 
lunar craters are really 
the result of volcanic 
eruptions, they must be 
ancient formations, for 
there is no satisfactory 
evidence of any present 
volcanic activity. Fig. 2 "] 
represents one of the 
finest lunar craters, Gas- 
sen di, about fifty-six 
miles in diameter, which 
is best seen about two 
days after the half- 
moon. 

154. Other Lunar 
Formations. — The 
craters and mount- 
ains are not the only 
interesting features 
on the moon's sur- 
face. There are many 
which go by the name of " rills," and may once have been 
watercourses. (See Fig. 24.) Then there are many straight 
" clefts " half a mile or so wide, and of unknown depth, 
running in some cases several hundred miles straight 
through mountain and valley, without any apparent regard 
to the accidents of the surface. 




Fig. 24. — Copernicus 

deep, narrow, crooked valleys 



124 LESSONS m ASTRONOMY 

Most curious of all are the light-colored streaks, or 
"rays," which radiate from certain of the craters, extend- 
ing in some cases a distance of many hundred miles. 
They are usually from five to ten miles wide, and neither 
elevated nor depressed to any considerable extent with 
reference to the general surface. Like the clefts, they 
pass across valley and mountain, and sometimes straight 
through craters, without any change in width or color. 
No satisfactory explanation of them has yet been given. 
The most remarkable of these " ray-systems " is the one 
connected with the great crater Tycho, not very far from 
the moon's south pole. The rays are not very conspicuous 
until within a few days of full moon, but at that time they, 
and the crater from which they diverge, constitute by far 
the most striking feature of the telescopic view. 

155. Changes on the Moon. — It is certain that there 
are no conspicuous changes on the moon's surface ; no such 
transformations as would be presented by the earth viewed 
with a telescope from the moon, — no clouds, no storms, 
no snow of winter, and no spread of verdure in the spring. 
At the same time it is confidently maintained by some 
observers that here and there perceptible alterations do 
take place in the details of the lunar surface. Professor 
W. H. Pickering, the younger brother of the Director of 
the Harvard Observatory, is at present the most prominent 
supporter of this view. 

The difficulty in settling the question arises from the 
great changes which take place in the appearance of a 
lunar object, according to the angle at which the sunlight 
strikes it. Other conditions also, such as the height of the 
moon above the horizon and the clearness and steadiness 



LUNAR MAPS AND NOMENCLATURE 125 

of the air, affect the appearance ; and it is very difficult to 
secure a sufficient identity of conditions at different times 
of observation to be sure that apparent changes are real. 
It is probable that the question will finally be settled by 
photography. (For further discussion of this subject, see 
General Astronomy, Art. 272.) 

156. Lunar Maps and Nomenclature. — A number of 
maps of the moon have been constructed by different 
observers. The most recent and extensive is that by 
Schmidt of Athens, on a scale of seven feet in diameter ; 
it was published by the Prussian government in 1878. 
Perhaps the best for ordinary observers is that given in 
Webb's " Celestial Objects for Common Telescopes." We 
present here (Fig. 25) a skeleton map, which indicates the 
position of about fifty of the leading objects. 

As for the names of the lunar objects, the great plains 
upon the surface were called by Galileo " oceans," or " seas" 
(Maria), because he supposed that these grayish surfaces, 
which are visible to the naked eye and conspicuous in a 
small telescope, though not with a large one, were covered 
with water. Thus we have the " Oceanus Procellarum" 
(Sea of Storms) and " Mare Imbrium " (Sea of Showers). 
The ten mountain ranges on the moon are mostly named 
for terrestrial mountains, as Caucasus, Alps, Apennines, 
though two or three bear the names of astronomers, like 
Leibnitz, Doerfel, etc. The conspicuous craters bear the 
names of ancient and mediaeval astronomers and philoso- 
phers, as Plato, Archimedes, Tycho, Copernicus, Kepler, 
and Gassendi. This system of nomenclature seems to 
have originated with Riccioli, who made the first map of 
the moon in 1650. 



126 



LESSONS IN ASTRONOMY 



156*. Lunar Photography. — The earliest success in lunar 
photography was that of W. C. Bond at Cambridge (U.S.) 
in 1850, using the old daguerreotype process. This was 




Fig. 25. — Map of the Moon, reduced from Neison 

soon followed by the work of De la Rue in England, and a 
little later by Dr. Henry Draper and Lewis M. Rutherfurd 
in New York. Until very lately Mr. Rutherfurd's pictures 
remained unrivaled ; but since 1890 there has beep, a great 



LUNAR PHOTOGRAPHY 



127 



advance. At various places, especially at Cambridge and 
the Lick and Yerkes observatories in this country, and at 
Paris, most admirable photographs have been made which 
bear enlargement well, and show details almost (not quite) 
as perfectly as they can be seen with the telescope. 
Already maps of the lunar surface have been made from 
them exceeding in accuracy even the great map of Schmidt 
mentioned in the preceding article. 



Key to the Principal Objects indicated in Fig. 25 



A. Mare Humor urn. 

B. Mare Xectaris. 

C. Oceanus Procellarum. 

D. Mare Fecunditatis. 

E. Mare Tranquilitatis. 

F. Mare Crisium. 

G. Mare Serenitatis. 
H. Mare Tmbrium. 

/. Sinus Tridum. 



K. Mare Nubium. 

L. Mare Frigoris. 

T. Leibnitz Mountains. 

U. Doerfel Mountains. 

V. Rook Mountains. 

W. D'Alembert Mountains. 

X. Apennines. 

Y. Caucasus. 

Z. Alps. 



1. Clavius. 

2. Schiller. 

3. Maginus. 

4. Schickard. 

5. Tycho. 

6. Walt her. 

7. Purbach. 

8. Petavius. 

9. "The Railway." 

10. Arzachel. 

11. Gassendi. 

12. Catherina, 

13. Cyrillus. 



14. Alphonsus. 

15. Theophilus. 

16. Ptolemy. 

17. Langrenus. 

18. Hipparchus. 

19. Grimaldi. 

20. Flamsteed. 

21. Messier. 

22. Maskelyne. 

23. Triesnecker. 

24. Kepler. 

25. Copernicus. 

26. Stadius. 



27. Eratosthenes. 

28. Proems. 
28 / . Pliny. 

29. Aristarchus. 

30. Herodotus. 

31. Archimedes. 

32. Cleomedes. 

33. Aristillus. 

34. Eudoxus. 

35. Plato. 

36. Aristotle. 

37. Endymion. 



128 LESSONS IX ASTRONOMY 

The half-tone engraving which forms the frontispiece is from two 
photographs, the first of which, of the moon a little past the full, 
was made by Professor Hale in 1892 at his Kenwood Observatory in 
Chicago ; the other is enlarged from a magnificent photograph made 
by Ritchey with the non-photographic forty-inch telescope of the 
Yerkes Observatory, a yellowish color-screen being interposed in 
front of the sensitive plate to cut off the red, violet, and ultra-violet 
rays in accordance with a suggestion by Professor Hale. The 
original negative, about six inches in diameter, is certainly unsur- 
passed by any hitherto made with photographic lenses or reflectors. 
The portion shown includes the great crater Theophilus, 60 miles 
in diameter and 17,000 feet deep, with its neighbors Cyrillus and 
Catherina. 

The reader will notice the relative ages of the craters. On 
the moon the deepest craters and the highest mountains are the 
youngest, as is the case with the mountains on the earth. The 
Himalayas, the Alps, and the Andes are infants compared with 
the Laurentian range, now low because worn down by time. 



CHAPTER VI 

THE SUN AND SPECTROSCOPE 

Its Distance, Dimensions, Mass, and Density — Its Rotation, Surface, and 
Spots — The Spectroscope and the Chemical Constitution of the Sun — 
The Chromosphere and Prominences — The Corona — The Sun's Light — 
Measurement and Intensity of the Sun's Heat — Theory of its Maintenance 
and Speculations regarding the Age of the Sun 

157. The sun is a star, the nearest of them — a hot, 
self-luminous globe, enormous as compared with the earth 
and moon, though probably only of medium size as a star ; 
but to the earth and the other planets which circle around 
it, it is the grandest and most important of all the heav- 
enly bodies. Its attraction controls their motions, and its 
rays supply the energy which maintains every form of 
activity upon their surfaces. 

158. The Sun's Distance. — The mean distance of the 
sun from the earth (the astronomical unit of distance) is a 
little less than 93,000000 miles. There are many methods 
of determining it, some of which depend on a knowledge of 
the Velocity of Light (Appendix, Sees. 434 and 436), while 
others depend on finding the sun's horizontal parallax. 
(For a resume of the subject, see General Astronomy, 
Chap. XIV, or Chap. XV of the Manual of Astronomy.) 
The mean value of this parallax is very nearly 8".8. In 
other words, as seen from the sun, the earth has an 
apparent diameter of about 17". 6 (Sec. 139). The dis- 
tance is variable, to the extent of about 1,500000 miles, 

129 



130 LESSONS m ASTRONOMY 

on account of the eccentricity of the earth's orbit, the 
earth being almost 3,000000 miles nearer to the sun on 
December 31 than on July 1. 

Knowing the distance of the earth from the sun, the 
earth's orbital velocity follows at once by dividing the cir- 
cumference of the orbit by the number of seconds in a 
year. It comes out 18.5 miles per second. (Compare this 
with the velocity of a cannon-ball, which seldom exceeds 
2500 feet per second.) In traveling this 18i miles, the 
deflection of the earth's motion from a perfectly straight line 
amounts to less than one-ninth of an inch. 

159. The distance of the sun is of course enormous compared 
with any distance upon the earth's surface. Perhaps the simplest 
illustration which will give us any conception of it is that drawn 
from the motion of a railway train, which, going a thousand miles 
a day (nearly forty-two miles an hour without stops) would take 
254^ years to make the journey. If sound were transmitted through 
interplanetary space, and at the same rate as in our own air, it would 
make the passage in about fourteen years ; i.e., an explosion on the 
sun would be heard by us fourteen years after it actually occurred. 
Light traverses the distance in 499 seconds. 

160. Dimensions of the Sun. — The sun's mean apparent 
diameter is 33' 4". Since at its mean distance V 1 equals 
450.36 miles, its diameter is 866,500 miles, or 109i times 
that of the earth. If we suppose the sun to be hollowed 
out, and the earth placed at the center of it, the sun's 
surface would be 433,000 miles away. Now, since the 
distance of the moon from the earth is about 239,000 miles, 
she would be only a little more than half-way out from 
the earth to the inner surface of the hollow globe, which 
would thus form a very good background for the study of 
the lunar motions. 



THE SUN'S DIMENSIONS, MASS, AND DENSITY 131 

If we represent the sun by a globe two feet in diameter, the earth 
on the same scale would be 0.22 of an inch in diameter, the size of 
a very small pea. Its distance from the sun would be just about 
220 feet, and the nearest star, still on the same scale, would be 8000 
miles away, on the other side of the earth. 

Since the surfaces of globes are proportional to the 
squares of their radii, the surface of the sun exceeds 
that of the earth in the ratio of (109. 5) 2 : 1; i.e., the 
area of its surface is about 12,000 times the surface of 
the earth. 

The volumes of spheres are proportional to the cubes of 
their radii; hence the sun's volume, or bulk, is (109.5) 3 , or 
1,300000 times that of the earth. 

161. The Sun's Mass, Density, and Superficial Gravity. — 
The mass of the sun is about 332,000 times that of the 
earth. There are various ways of getting at this result, but 
they lie rather beyond the mathematical scope of this work. 

Its density, as compared with that of the earth, is found 
by simply dividing its mass by its bulk (both as compared 
with the earth) ; i.e., the sun's density equals fVVVoVV 
= 0.255, — a little more than a quarter of the earth's density. 

To get its specific gravity (i.e., its density compared 
with water), we must multiply this by the earth's mean 
specific gravity, 5.53. This gives 1.41. In other words, 
the sun's mean density is only about 1.4 times that of 
water, — a very significant result as bearing on its physical 
condition, especially when we know that a considerable 
portion of its mass is composed of metals. 

Of course this low density depends upon the fact that the tem- 
perature is enormously high and the materials are mainly in a state 
of cloud, vapor, or gas. 



132 



LESSONS IN ASTRONOMY 



The superficial gravity is about 27.6 as great as gravity 
on the earth ; that is to say, a body which weighs one pound 
on the surface of the earth would there weigh 27.6 pounds, 
and a person who weighs 150 pounds here would there 
weigh nearly two tons. A body would fall 444 feet in the 
first second, and a pendulum which vibrates seconds on the 
earth would vibrate in less than a fifth of a second there. 
162. The Sun's Rotation. — Dark spots are often visible 
upon the sun's surface, passing across the disk from east 

to west and indicating an 
axial rotation. The aver- 
age time occupied by a 
spot in passing around 
the sun and returning to 
the same apparent posi- 
tion, as seen from the 
earth, is about 27.25 days; 
different observers, how- 
ever, get slightly different 
results, because, as we 
shall see, the spots are 
not firmly attached to the 
sun's surface, but drift 
about to some extent. This interval, however, is not 
the true time of the sun's rotation, but the synodic, as is 
evident from Fig. 26. Suppose an observer on the earth 
at E sees a spot on the center of the sun's disk at S; while 
the sun rotates E will also move forward in its orbit, and 
the observer, the next time he sees the spot on the center 
of the disk, will be at E r , the spot having gone around 
the whole circumference plus the arc SS f . 




Fig. 26. - 



- Synodic and Sidereal Revolu- 
tions of the Sun 



THE SUN'S ROTATION 133 

The equation by which the true, or sidereal, period is deduced from 
the synodic is the same as in the case of the moon, viz. : 

1 _I_ 1_, 
S~ T e' 

T being the true period of the sun's rotation, E the length of the 
year, and *S the observed synodic rotation. This gives T — 25.35. 

The paths of the spots across the sun's disk are usually 
more or less oval, showing that the sun's axis is inclined 
to the ecliptic, and so inclined that the north pole is tipped 
about 74° towards the position which the earth occupies 




December 6 th March 6** June 5** September 5th 

Fig. 27. — Spot Belts and Paths 

near the 1st of September. Twice a year the paths 
become straight, when the earth is in the plane of the 
sun's equator, June 3 and December 5 (Fig. 27). 

163. Peculiar Law of the Sun's Rotation. — It was 
noticed quite early that different spots give different 
results for the period of rotation, but the researches of 
Carrington, about thirty years ago, first brought out the 
fact that the differences are largely systematic, so that at 
the solar equator the time of solar rotation is less than on 
either side of it. For spots near the sun's equator it is 
about 25 days; for solar latitude 30°, 26.5 days ; and in 
solar latitude 40°, 27 days. The time of rotation of the sun's 
surface in latitude 45° is fully two days longer than at the 



134 



LESSONS IN ASTRONOMY 



equator ; but we are unable to follow the law further towards 
the poles of the sun, because spots are almost never found 
beyond the parallel of 45°, though faculse which have been 
observed in higher latitudes corroborate the result in a 
general way, as do certain spectroscopic observations. 

Possibly this equatorial acceleration may be due in some way to 
the tremendous outpour of heat from the solar surface, as Emden 
has attempted to show in a recent paper. The more general impres- 
sion is, however, that it is due not 
to any causes now operating, but is a 
lingering survival from the sun's past 
history, and destined ultimately to 
disappear; 




Fig. 28. — Telescope and Screen 



164. Study of the Sun's Sur- 
face. — The heat and light of 
the sun are so intense that we 
cannot look directly at it with 
a telescope, as we do at the moon, and it is necessary, 
therefore, to provide either a special eyepiece with suit- 
able shade-glass, or arrange the telescope, as in Fig. 28, 
so as to throw an image of the sun upon a screen. 

In the study of the sun's surface, photography is for 
some purposes very advantageous and much used. The 
instrument must, however, have lenses specially constructed 
for photographic operations, since an object-glass which 
would give admirable results for visual purposes would 
be worthless photographically. Since 1890, however, a 
few object-glasses have been made with new kinds of 
glass, which are said to be good both for photography 
and lor the eye. The exposure required for a photograph 
is practically instantaneous. The negatives arc usually 



STUDY OF THE SUN'S SURFACE 



135 



from two inches to eight or ten in diameter, and some of 
the best of them bear enlarging to forty inches. 

Photographs have the great advantage of freedom from prepos- 
session on the part of the observer, and in an instant of time they 
secure a picture of the whole surface of the sun such as would require 




Fig. 20. — Greenwich Photograph of Sun, Sept. 10, 1808 

a skillful draftsman hours to copy. But, on the other hand, they 
take no advantage of the instants of fine seeing, but represent the 
solar surface as it happened to appear at the moment when the 
plate was uncovered, affected by all the momentary distortions due 
to atmospheric disturbances. 



136 LESSONS IN ASTRONOMY 

165. The Photosphere. — The sun's surface seen with a 
telescope, under a medium magnifying power, appears to be 
of nearly uniform texture, though distinctly darker at the 
edges, and usually marked here and there with certain dark 




Fig. 30. — Nodules and Granules on the Sun's Surface 
After Langley 

spots. With a higher power it is evident that the visible 
surface (called the photosphere) is by no means uniform, 
but is made up, as shown in Fig. 30, of a comparatively 
darkish background sprinkled over with grains, or "nod- 
ules," as Herschel calls them, of something more brilliant, — 






THE PHOTOSPHERE AXD FACULJE 



137 



"like snowflakes on a gray cloth," according to Langley. 
These nodules, or "rice grains," are from 400 to 600 miles 
across, and, when the seeing is best, themselves break up 
into more minute " granules." For the most part, the 
nodules are about as broad as they are long, though of 
irregular form ; but here and there, especially in the 
neighborhood of the spots, they are drawn out into long 
streaks, known as " filaments," " willow leaves," or " thatch 
straws." 

Certain bright streaks called "facute" are also usually 
visible here and there upon the sun's surface, and though 
not very obvious 
near the center 
of the disk, they 
become con- 
spicuous near 
the " limb," or 
edge, of the disk, 
especially in the 
neighborhood 
of the spots, 
as shown in 
Fig. 31. These 
faculae are masses of the same material as the rest of 
the photosphere, but elevated above the general level 
and intensified in brightness. When one of them passes 
off the edge of the disk, it is sometimes seen as a little 
projection. The fact, however, that their spectrum shows 
bright lines of calcium vapor makes it uncertain whether 
they may not be clouds of that substance floating high 
above the photosphere. 




Fig. 31. — Spots and Faculae 
After De la Rue 



138 



LESSONS IN ASTRONOMY 



In their nature, the photospheric nodules and faculse 
are generally believed to be luminous clouds, floating in a 
less luminous atmosphere, just as a snow or rain cloud, 
which has been formed by the condensation of water- 
vapor, floats in the earth's atmosphere. Such a cloud, 
while at a temperature even lower than that of the sur- 
rounding gases, has a vastly greater power of emitting 

light, and therefore, 
like the " mantle " 
of a Welsbach gas- 
burner, appears very 
brilliant in compari- 
son with the gas in 
which it floats. 
There is consider- 
able probability that 
the principal ele- 
ment in the photo- 
sphere is carbon. 
There are, however, 
some serious diffi- 
culties with this 
cloud th eory, 
which may or may 
not be removed by further investigation. 

166. Sun-Spots. — Sun-spots, whenever visible, are the 
most interesting and conspicuous objects upon the solar 
surface. The appearance of a normal sun-spot (Fig. 32), 
fully formed and not yet beginning to break up, is that 
of a dark central " umbra," more or less circular, with a 
fringing " penumbra " composed of converging filaments. 







Fig. 32. — Normal Sun-Spot 
After Secchi 



SUN-SPOTS 



139 



The umbra itself is not uniformly dark throughout, but is 
overlaid with filmy clouds, which usually are rather hard 
to see, but sometimes are conspicuous, as in the figure. 
Usually, also, within the umbra there are a number of 
round and very black spots, sometimes called " vortices," 
but often referred to as " Dawes's holes," after the name 
of their first discoverer. 

Even the darkest portions of the umbra, however, are 
dark only by contrast. Photometric observations show 




Fig. 33. — Group of Spots from a Greenwich Photograph, Sept. 11, 1898 

that the nucleus of a spot gives about one per cent as 
much light as a corresponding area of the photosphere ; 
the blackest portion of a sun-spot is really more brilliant 
than a calcium light. 

Very few spots are strictly normal. Frequently the 
umbra is out of the center of the penumbra, or has a 



140 LESSONS IN ASTRONOMY 

penumbra on one side only, and the penumbral filaments, 
instead of converging regularly towards the nucleus, are 
often distorted in every conceivable way. Spots are often 
gathered in groups within a common penumbra, separated 
from each other by brilliant " bridges," which extend across 
from the outside photosphere. Occasionally a spot has no 
penumbra at all, and sometimes we have what are called 
" veiled " spots, in which there seems to be a penumbra 
without any central nucleus. 

167. Nature of Sun-Spots. — The spots are probably 
shallow depressions, or hollows, in the photosphere, filled with 
gases and vapors, which are cooler than the surrounding 
regions, and therefore absorb a considerable portion of 
light, and make the spot look dark. The evidence that 
they are depressions consists in the change in their appear- 
ance as they approach the " limb," or edge, of the disk. 
Here the penumbra becomes wider on the outer edge and 
narrower on the inner edge, and just before the spot goes 
out of sight around the edge of the sun the penumbra on 
the inner edge entirely disappears. The appearance is pre- 
cisely such as would be shown by a saucer-shaped cavity 
in the surface of a globe, the bottom of the cavity being 
painted black to represent the umbra, and the sloping 
sides gray for the penumbra. (See Fig. 34.) 

Observations upon a single spot would hardly be sufficient to 
prove this, because the spots are so irregular in their form ; but by 
observing the behavior of several hundred, the truth appears in the 
average result. Occasionally, when a very large spot passes off the 
sun's limb, a depression can be seen with the telescope. It is only 
fair to add, however, that some observers of great experience still 
dispute the received theory, and maintain that spots are dark clouds 
of some kind floating on, or just above, the photosphere. 



NATURE AND DIMENSIONS OF SUN-SPOTS 141 

That the nucleus of a spot is generally cooler as well as 
darker than the rest of the sun's surface, has been proved 
by several observers by direct experiments, though very 
near the edge of the sun the reverse has been found to be 
the case in some instances. 

The penumbra is usually composed of " thatch straws," 
or long-drawn-out filaments, and these, as has been said, 
converge in a general way towards the center of the 



Fig. 34. — Sun-Spots as Cavities 

spot. In the neighborhood of the spot the surrounding 
photosphere is usually much disturbed and elevated into 
faculae. 

168. Dimensions of Sun-Spots, etc. — The diameter of 
the umbra of a sun-spot varies all the way from 500 miles, 
in the case of a very small one, to 50,000 miles in the case 
of a very large one. The penumbra surrounding a group 
of spots is sometimes 150,000 miles across, though that is 
an exceptional size. Quite frequently sun-spots are large 
enough to be visible with the naked eye, and can actually 
be thus seen at sunset or through a fog, or by the help 
of a colored shade-glass. The depth of the bottom of a 
spot is very difficult to determine, but according to Faye, 
Carrington, and some others, it seldom exceeds 2500 miles, 
and more often is between 500 and 1500. 



142 LESSONS IN ASTRONOMY 

The duration of sun-spots varies greatly, but they are 
always short-lived phenomena from the astronomical point 
of view, sometimes lasting only for a few days, though 
more frequently for a month or two. In one instance a 
spot group attained the age of eighteen months. 

As to their cause, positive knowledge is still wanting. 
Numerous theories, more or less satisfactory, have been 
proposed. On the whole, perhaps the most probable view 
is that they are the effect of eruptions breaking through 
the photosphere. It is not likely, however, that they are 
the holes, or craters, through which the eruptions break 
out, as Secchi at one time thought, and as Mr. Proctor 
maintained to the very last; it is more probable, in 
accordance with Secchi's later views, that when an erup^ 
tion takes place, a hollow, or sink, results in the neigh, 
boring cloud-surface, and in this hollow the cooler gases 
and vapors collect. It is almost universally admitted that 
in some way they are due to matter descending from above 
upon the photosphere, but there is wide difference of opinion 
as to the nature and source of the falling substance, — 
whether it is meteoric, or was formed by condensation in 
the upper regions of the solar atmosphere, or thrown up 
from under the photosphere by eruption, as just suggested. 

169. Distribution of Spots, and their Periodicity. — It is 
a significant fact that the spots are confined mostly to two 
zones of the sun's surface between 5° and 40° of north 
and south solar latitude. Practically none are ever found 
beyond the latitude of 45°, but at the time when spots are 
most numerous a few appear near the equator. 

In 1843 Schwabe of Dessau, by the comparison of an 
extensive series of observations covering nearly twenty 



PERIODICITY OF SUN-SPOTS 143 

years, showed that the sun-spots are probably periodic, 
being at some times much more numerous than at others* 
with a roughly regular recurrence every ten or eleven 
years. A few years later he fully established this remark- 
able result. Wolf of Zurich has collected all the observa- 
tions discoverable, and has obtained a pretty complete 
record back to 1610, when Galileo first discovered these 
objects. The average period is 11.1 years, but the maxima 
are somewhat irregular, both in time and as to the extent 
of the surface covered by spots. The last maximum 
occurred in 1900-1901. 

During the maximum the sun is never without spots, 
from twenty-five to fifty being visible at once. During 
the minimum, on the contrary, weeks and even months 
pass without the appearance of a single one. The cause 
of this periodicity is not yet known. 

Another curious and important fact has recently been brought 
out by Spoerer, though not yet explained. Speaking broadly, the 
disturbance which produces the spots of a given period first mani- 
fests itself in two belts, about 30° north and south of the sun's 
equator. These belts then draw in towards the equator, and the 
spot-maximum occurs when their latitude is about 16°; while the 
disturbance finally dies out at a latitude of from 5° to 10°, about 
twelve or fourteen years after its first outbreak. Two or three years 
before this disappearance, however, two new zones of disturbance 
show themselves. Thus, at the spot-minimum there are usually four 
well-marked spot-belts : two near the sun's equator, due to the expir- 
ing disturbance, and two in high latitudes, due to the newly begin- 
ning outbreak. 

170. Terrestrial Influence of Sun-Spots One influence 

of sun-spots on the earth is perfectly demonstrated. 
When the spots are numerous, magnetic disturbances 



144 LESSONS m ASTRONOMY 

(magnetic storms) are most numerous and most violent upon 
the earth, — a fact not to be wondered at, since notable 
disturbances upon the sun's surface have been immediately 
followed by magnetic storms with brilliant exhibitions of 
the Aurora Borealis, as in 1859 and 1883. But no one 
has yet been able to explain the nature of the connection 
between disturbances upon the sun's surface and those of 
terrestrial magnetism : we do not know whether the solar 
disturbance is the cause or occasion of the terrestrial, or 
whether they are merely simultaneous effects of some 
external influence, though the fact is beyond doubt. 

It has been attempted, also, to show that the periodical disturbance 
of the sun's surface is accompanied by effects upon the earth's mete- 
orology, — upon its temperature, barometric pressure, storminess, 
and the amount of rainfall. On the whole, it can only be said that 
while it is possible and even probable that real effects are produced, 
they must be very slight, and are almost entirely covered up by the 
effect of purely terrestrial causes. The results obtained thus far 
in attempting to coordinate sun-spot phenomena with meteorological 
phenomena are unsatisfactory and often contradictory. We may add 
that the spots cannot produce any sensible effect by their direct action 
in diminishing the light and heat of the sun. They do not directly 
alter the amount of solar radiation at any time by so much as one 
part in a thousand. 

THE SOLAR SPECTRUM AND ITS REVELATIONS 

About 1860 the spectroscope appeared in the field as a 
new and powerful instrument for astronomical research, 
resolving at a glance many problems which before did not 
seem even open to investigation. It is not extravagant 
to say that its invention has done almost as much for 
astronomy as that of the telescope itself. 



PRINCIPLE OF THE SPECTROSCOPE 145 

It enables us to study the light of distant objects and 
read therein a record more or less complete of their 
chemical composition and physical conditions ; also to 
measure the speed with which they are approaching or 
receding, and sometimes, as in the case of the solar promi- 
nences, to observe at any time objects otherwise visible 
only on rare occasions. The spectroscope and its close 
ally, the photographic plate, have together given us "the 
New Astronomy." 

171. Principle of the Spectroscope. — The essential part 
of the apparatus is either a prism or a train of prisms, or 
else a diffraction " grating," 1 which is capable of perform- 
ing the same office of " dispersing " (i.e r of spreading and 
sending in different directions) the rays of different colors 
and wave-lengths. 

If with such a " dispersion piece," as we may call it 
(either prism or grating), one looks at a distant point of 
light, he will see instead of a point a long, bright streak, 
red at one end and violet at the other. If the object 
looked at is a line of light, parallel to the edge of the 
prism or to the lines of the grating, then instead of a 
colored streak without width, he gets a colored band or 
ribbon of light, the spectrum, which may show markings 
that will give him much valuable information. It is 
usual to form this line of light by admitting the rays 
through a narrow " slit " placed at one end of a tube, 
which carries at the other end an achromatic object-glass 
having the slit in the principal focus. This tube, with 

a The "grating" is merely a piece of glass or speculum metal, ruled 
with many thousand straight, equidistant lines, from 5000 to 20,000 in 
the inch. 



146 



LESSONS IN ASTRONOMY 



slit and lens, constitutes the "collimator." Instead of 
looking at the spectrum with the naked eye, it is better 
also in most cases to use a small " view telescope," so 
called to distinguish it from the large telescope to which 
the spectroscope is often attached. 

172. Construction of the Spectroscope. — The instrument, 
therefore, as usually constructed, and shown in Fig. 35, 



Prism Spectroscope 




Grating 



\s 3 



Direct-Vision Spectroscope 
Fig. 35.— Different Forms of Spectroscope 

consists of three parts, — collimator, dispersion piece, and 
view telescope, — although in the " direct-vision " spectro- 
scope, shown in the figure, the view telescope is omitted. 
If the slit S be illuminated by strictly homogeneous light 
(i.e., light all of one color), say yellow, the "real image" 
of the slit will be found at Y. If, at the same time, light 
of a different color — red, for instance — be also admitted, 






THE SOLAR SPECTRUM 



147 



a second image will be formed at B, and the observer will 
then see a spectrum consisting of two bright lines, one 
yellow, the other red, which are really nothing more than 
images of the slit. 

If violet light be admitted, a third image will be formed 
at F, and there will be three bright lines. If light from 
a candle be admitted, there will be an infinite number of 
these slit-images close together, like the pickets in a fence, 
without interval or break, and we then get what is called 
a "continuous" spectrum. 

If, however, we look at sunlight or moonlight or the light 
of a star, we shall find a spectrum continuous in the main, 

63 b 2 &i E 






Fig. 36. — Small Portion of Solar Spectrum (green) 
Photographed by Higgs 

but crossed by thousands of dark lines, or missing slit-images 
(as if some of the fence pickets had been destroyed, leav- 
ing gaps in the series). The cause of these dark lines, 
first noticed by Wollaston in 1800, but later and inde- 
pendently discovered and carefully observed by Fraunhofer 
in 1814, was a mystery for nearly fifty years, until the 
epoch-making work of Kirchhoff. 

173. Principles upon which Spectrum Analysis depends. — 
These, substantially, as announced by Kirchhoff in 1858, 
are the three following : 

1. A continuous spectrum is given by bodies which are so 
dense that the molecules interfere with each other in such a 



148 LESSONS m ASTRONOMY 

way as to prevent their free vibration ; i.e., by bodies which 
are either solid or liquid, or, if gaseous, are under pressure. 

2. The spectrum of a luminous gas under low pressure 
is discontinuous, that is, it is made up of bright lines or 
bands, and these lines are characteristic. The same sub- 
stance under similar conditions always gives the same set 
of lines, and usually it does so even under conditions which 
differ rather widely; but when the circumstances differ 
too much, it may give two or more different spectra. 

3 (and most important for our purpose just now). A 
gas or vapor absorbs from a beam of white light passing 
through it precisely those rays of which its own spectrum con- 
sists ; so that the spectrum of white light which has been 
transmitted through such a vapor, if the vapor is cooler 
than the original source of light, exhibits a "reversed" 
spectrum of the gas ; i.e., we get a spectrum which shows 
dark lines in place of the characteristic bright lines, as in 
the spectrum of sunlight. 

We therefore infer that the sun is covered by an 
envelope of gases, not so hot as the luminous clouds 
which form the photosphere, and that these gases by their 
absorption produce the dark lines in its spectrum. 

174. Experiment illustrating Reversal of Spectrum. — 
The principle of reversal is illustrated by Fig. 37. Sup- 
pose that in front of the spectroscope we place a spirit lamp 
with a little carbonate of soda and some salt of thallium 
upon the wick. We shall then get a spectrum showing the 
two yellow lines of sodium and the green line of thallium, all 
bright, as in the upper of the two spectra. If now the lime- 
light be started behind the flame, we shall at once get the 
effect shown in the lower figure. — a continuous spectrum 



REVERSAL OF SPECTRUM LINES 



149 



Reversal of Spectrum 






crossed by three black lines which exactly replace the 
brighter ones. Thrust a screen between the lamp flame and 
the lime, and the dark lines instantly turn bright again. 

The dark lines which appear when the screen is removed are dark 
only relatively to the background: when the screen is taken away they 
really brighten a 
little (say two or 
three per cent); 
but the brightness 
of the background 
increases hundreds 
of times, and so far 
exceeds that of the 
lines themselves 
that they look 
black. The dark 
lines of the solar 
spectrum are really 
bright, and can be 
photographed as 
such by arranging 
matters so that 
one of them shall 
fall upon a nar- 
row slit in a diaphragm which excludes all the brighter background. 

175. Chemical Constituents of the Solar Atmosphere. — 
By taking advantage of these principles we can detect 
a large number of well-known terrestrial elements in 
the sun by means of the dark lines 1 in its spectrum, 

1 They are generally referred to as Fraunhofer's lines, because Fraun- 
hofer was the first to map them. To some of the principal ones he 
assigned letters of the alphabet, which are still retained ; thus, A is a 
strong red line at the extreme end of the spectrum ; C, one in the scarlet ; 
D, one in the yellow ; and JT, one in the violet. 




Fig. 37. — Reversal of the Spectrum 



150 



LESSONS m ASTRONOMY 



which, in an instrument of high power, number several 
thousand. 

By proper arrangements it is possible to identify among 
these lines many which are due to the presence in the sun's 
atmosphere of known terrestrial elements in the state of 
vapor. To effect the comparison necessan^ for this purpose, 
the spectroscope must be so arranged that the observer can 
confront the spectrum of sunlight with that of the sub- 
stance to be tested. In order to do this, half of the slit is 
covered by a little reflector, or " comparison prism," which 
reflects into the tube the light of the sun, while the other 




Fig. 38. — Photographic Comparison of the Solar Spectrum with that of Iron 

Trowbridge 

half of the slit receives directly the light of some flame 
or electric spark. On looking into the spectroscope the 
observer will then see a spectrum, the lower half of which, 
for instance, is made by sunlight, while the upper half is 
made by light coming from an electric spark between two 
metal points, say of iron. This latter spectrum will show 
the bright lines of iron vapor, and the observer can then 
easily see whether they do or do not correspond exactly 
with the dark lines of the solar spectrum. 

In such comparisons photography may be most effectively used 
instead of the eye. Fig. 38 is an excellent reproduction, on a reduced 
scale, of a negative made by Professor Trowbridge of Cambridge. 



ELEMENTS DISCOVERED IN THE SUN 



151 



The lower half is the violet portion of the sun's spectrum, and the 
upper half the corresponding portion of that of an electric arc charged 
with the vapor of iron. (In the negative the dark lines, of course, are 
bright, and vice versa.} The reader can see for himself w r ith what 
absolute certainty such a photograph indicates the presence of iron 
in the solar atmosphere. A few of the lines in the photograph which 
do not show corresponding lines in the solar spectrum are due to 
other substances than iron. 

176. Elements known to exist in the Sun. — As the result 
of such comparisons we have the following list of thirty- 
six elements which are now known to exist in the sun. 



* Calcium, 11. 
*Iron, 1. 

* Hydrogen, 22. 

* Sodium, 20. 
*Xickel, 2. 

* Magnesium, 19. 

* Cobalt, 6. 
Silicon, 21. 
Aluminium, 25. 

* Titanium, 3. 

* Chromium, 5. 

* Manganese, 4. 



Copper, 30. 
Zinc, 29. 
Cadmium, 26. 
* Cerium, 10. 
Glucinum, 33. 
Germanium, 32. 
Rhodium, 27. 
Silver, 31. 
Tin, 34. 
Lead, 35. 
Erbium, 28. 
Potassium, 36. 



* Strontium, 23. 
Vanadium, 8. 

* Barium, 24. 
Carbon, 7. 
Scandium, 12. 
Yttrium, 15. 
Zirconium, 9. 
Molybdenum, 17. 
Lanthanum, 14. 
Niobium, 16. 
Palladium, 18. 
Neodymium, 13. 

The substances are arranged according to the intensity of the dark 
lines by which they are represented in the solar spectrum, while the 
numbers appended indicate the rank which each would hold if the 
arrangement had been based upon the number of lines. An asterisk 
denotes that the lines of the element often or always appear as bright 
lines in the spectrum of the chromosphere (Sec. 180). To these 
elements must be added Helium (Sec. 181), which gives no dark 
lines in the spectrum of the photosphere, but does give several 
conspicuous bright lines in that of the chromosphere. 

In the atmosphere of the sun these bodies must be, of 
course, in the condition of vapor, which is somewhat cooler 



152 LESSONS IN ASTRONOMY 

than the clouds which form the photosphere. It will be 
noticed that all of them, carbon and hydrogen alone 
excepted, are metals, and that a number of the elements 
which are among the most important in the constitution 
of the earth fail to present themselves. Thus far nitrogen, 
chlorine, bromine, iodine, sulphur, phosphorus, and mer- 
cury all appear to be missing, and the indications of oxy- 
gen (which forms fully half the mass of the earth's crust) 
are very feeble and doubtful. 

We must be cautious, however, in drawing negative 
conclusions. It is quite possible that the spectra of these 
bodies under solar conditions may be so different from their 
spectra as presented in our laboratories, that we cannot 
easily recognize them : many substances, under different 
conditions, give two or more widely different spectra. 

177. The Reversing Layer. — According to Kirchhoff's 
theory, the dark lines are most of them 1 formed by the 
passing of light emitted by the minute solid or liquid 
particles of the photospheric clouds through the somewhat 
cooler vapors which compose the substances that we recog- 
nize by the dark lines in the spectrum. If this is so, the 
spectrum of the gaseous envelope, which by its absorption 
forms the dark lines, ought to show a spectrum of corre- 
sponding bright lines when seen by itself. The opportu- 
nities are rare when it is possible to obtain a spectrum of 

1 Among the thousands of lines in the solar spectrum a considerable 
number originate in the atmosphere of the earth. They are mostly due 
to oxygen and water-vapor, and are especially abundant in the red and 
yellow portions of the spectrum. These " telluric " lines are easily distin- 
guished by the fact that they become extremely conspicuous when the 
sun is near the horizon, but are feeble when he is near the zenith; and 
they also vary with the dryness of the air. 



THE REVERSING LAYER 153 

this gaseous envelope separate from that of the photo- 
sphere ; but at the time of a total eclipse, at the moment 
when the sun's disk has just been obscured by the moon, 
and the sun's atmosphere is still visible beyond the moon's 
limb, the observer ought to see this bright-line spectrum, 
if the slit of the spectroscope be carefully directed to the 
proper point ; and the observation has actually been made. 
The lines of the solar spectrum, which up to the time of the 
total obscuration of the sun remain dark as usual, are 
suddenly reversed, and the whole field of the spectroscope 
is filled with brilliant colored lines, which flash out quickly, 
and then gradually fade away, disappearing in about two 
seconds. 

The natural interpretation of this phenomenon is that 
the formation of the dark lines in the solar spectrum is, 
mainly at least, produced by a very thin stratum closely 
covering the photosphere, since the moon's motion in 
two seconds would correspond to a thickness of only 
500 miles. 

This observation, first made by the author in 1870, remained 
long uncorroborated, but received a beautiful photographic confirm- 
ation in 1896. Mr. Shackleton, the photographer of an English 
party which observed the eclipse of that year in Nova Zembla. 
obtained a photograph of the spectrum at the critical moment with 
an exposure of less than half a second, and found it just as described, 
showing several hundreds of bright lines which correspond to the 
dark Fraunhofer lines. A second photograph, made only five or 
six seconds later, shows only some twenty lines, well known as 
belonging to the spectrum of the chromosphere and prominences. 
Similar results for the " flash spectrum," as it is called, were also 
obtained by various observers during the eclipses of January, 1898, 
May, 1900, and May, 1901, with instruments of still higher power 
than that of Mr. Shackleton. 



154 



LESSONS IN ASTRONOMY 



There are reasons, however, to doubt whether the lines are all 
produced in such a thin layer. According to Sir Norman Lockyer, 
the solar atmosphere is very extensive, and certain lines of the spec- 
trum appear to be formed only in the regions of lower temperature 
high above the surface of the photosphere. It is probable also that 
many lines originate within the photosphere and not above it, being 
caused by the vapors which lie between the cloud masses that give 
the brilliant light. 

178. Sun-Spot Spectrum. — The spectrum of a sun-spot 
differs from the general solar spectrum not only in 
its diminished brilliancy, but in the great widening of 
certain lines, the thinning of others, and the change 
of some (especially the lines of hydrogen) to bright 

lines on some occasions. 
The majority of the Fraun- 
hofer lines, however, are 
not much affected either 



y 



way. 

In the green and blue 
FiG.sg.-TheC^iinej^ portions of the spectrum 

the darkest part of a sun- 
spot spectrum is found to be composed of fine dark 
lines close packed. This shows that the darkening is 
due to the absorption of light by gases and vapors, not 
by mist or smoke, for then the spectrum would be 
continuous. 

Sometimes, in connection with sun-spots, certain lines 
of the spectrum are bent and broken, as shown in 
Fig. 39. These distortions are explained by the swift 
motion towards or from the observer of the gaseous mat- 
ter, which by its absorption produces the line in question. 
In the case illustrated in the figure hydrogen was the 



DOPPLER-FIZEAU PRINCIPLE 



155 




substance, and its motion was from the observer, — nearly 
300 miles a second at one point. 

179. Doppler's Principle The principle upon which 

the explanation of this displacement and distortion of 
lines depends was first enunciated by Doppler in 1842. 
It is this : When the distance between us and a body which 
is emitting regular vibrations, either of sound or of light, is 
decreasing, then the number of pulsations received by us 
in each second is increased, and the length of the waves is 
correspondingly diminished. Thus, the pitch of a musical 
tone rises in the case 
supposed; and in the 
same way the refrangi- 
bility of a light-wave, 
which depends upon 
its wave-length, is in- 
creased, so that it will 
fall nearer the violet end of the spectrum. This principle 
finds numerous applications in modern astronomical spec- 
troscopy, and it is of extreme importance that the student 
should clearly understand it. In its astronomical applica- 
tions it is often called the Doppler-Fizeau principle because 
Fizeau first called attention to the shift that would be 
produced in the lines of a spectrum. 

Fig. 40 illustrates the principle. The lower strip is a small por- 
tion of the yellow part of the spectrum of an imaginary star, and 
the upper the corresponding part of the spectrum of sodium with 
which it is compared. The shift of the lines of the star spectrum 
indicates that it is coming nearer at the rate of nearly fifty miles 
a second ; some stars move faster. 

It was discovered in 1895, by Humphreys and Mohler at Baltimore, 
that increase of pressure causes the lines in the spectrum of a luminous 



Fig. 40. — The Doppler-Fizeau Principle 



156 LESSONS IN ASTRONOMY 

gas to shift slightly towards the red, very much as if the gas were 
receding, though not according to the same simple law. The shift is 
very slight, however, for pressures not exceeding 200 or 300 pounds to 
the inch ; but it is quite possible that in cases of explosion the pres- 
sures would be sufficient to cause large displacements. (See Sec. 355.) 

180. The Chromosphere. — Outside the photosphere, or 
shining surface of the sun, lies the so-called chromosphere, 
of which the stratum of gases that produce the dark lines 
in the solar spectrum is the hottest and densest portion. 
The word is derived from the Greek, chroma (color), and 
means " color sphere." It is so called because it is bril- 
liantly scarlet, owing this color to the hydrogen gas which 
is its most conspicuous component. In structure it is like 
a sea of flame covering the photosphere to a depth of from 
5000 to 10,000 miles, and seen through a telescope at the 
time of a total eclipse has been well described as looking 
like a " prairie on fire." There is, however, no real 
burning in the case, i.e., no heat-producing combination 
of hydrogen with oxygen or with any other element. 

Under ordinary circumstances the chromosphere is invisi- 
ble, drowned in the light of the photosphere. It can be 
seen with the telescope for only a few seconds at a time, 
during the fleeting moments of a total eclipse ; but with 
the spectroscope it can be studied at other times, as we 
shall see. 

181. Prominences and their Spectrum. — The promi- 
nences, or protuberances, are scarlet clouds which are seen 
during a total eclipse, projecting from behind the edge of 
the moon. They are simply extensions of the chromo- 
sphere, or isolated clouds of the same gaseous substances, 
chiefly hydrogen, their true nature having been established 



. 



THE PROMINENCES 157 

at an eclipse in 1868. when their spectrum was first satis- 
factorily observed. It is composed of numerous bright 
lines, conspicuous among which are the lines of hydrogen, 
together with a brilliant yellow line (sometimes called D 3 
because near the two so-called D lines) and the so-called H 
and K lines of calcium, with a number of others that are 
always present though more difficult to observe. At times 
also when the solar forces are peculiarly energetic hundreds 
of other lines appear, especially those of iron, titanium, 
magnesium, and sodium. 

For a long time the D 3 line remained entirely unidenti- 
fied, and the name of helium, or " sun-metal/' was proposed 
and accepted for the hypothetical element to which it was 
supposed to be due. In 1895. however. Dr. Ramsay, one 
of the discoverers of argon, found the D 3 line in the 
spectrum of a gas disengaged by heating and pumping 
from a rare mineral known as uraninite, and very soon 
the new gas was found by him and other observers in 
various other minerals and in meteoric iron. Along with 
the D 3 line were also found in the spectrum of the gas a 
number of other unidentified lines of the chromosphere 
spectrum, and these also appear with D 3 and the hydrogen" 
lines in the spectra of certain nebulae and stars. 

It was a great triumph thus to " run helium to earth," 
though as vet very little is known as to its nature and 
properties except that, next to hydrogen, it is the lightest 
of all known gases, in chemical inertness appears to 
resemble argon itself, and thus far is the only gas which 
resists liquefaction. 

182. Spectroscopic Observations of the Prominences and 
Chromosphere. — Since the spectrum of these objects is 



158 



LESSONS IN ASTRONOMY 



composed of a small number of brilliant lines, it is possible 
to observe tliem with a spectroscope in full daylight. The 
explanation of the way in which the spectroscope effects 
this lies rather beyond our limitations ; but it is sufficient 
for our purpose to say that by attaching a spectroscope 




Fig. 41. — Prominences 

1. Quiescent Prominences 2. Quiescent Prominences 

3. Eruptive Prominences — Flames 

4. Eruptive Prominences — Jets and Spikes near Sun's Limb, Oct. 5, 1871 

to a good telescope the prominences can now be studied 
at leisure any clear day. They are wonderfully interest- 
ing and beautiful objects. Some of them, the so-called 
" quiescent " prominences, are of enormous size, 50,000 or 
even 100,000 miles in height, faint and diffuse, remaining 



PHOTOGRAPHY OF PROMINENCES 159 

almost unchanged for days. Others are much more 
brilliant and active, especially those that are associated 
with sun-spots, as many of them are. These " eruptive " 
prominences often alter their appearance very rapidly, — 
so fast that one can sometimes actually see the motion : 
velocities from 50 to 200 miles a second are frequently 
met with. As a rule the eruptive prominences are not so 
large as the quiescent ones, but occasionally they surpass 




10.34 10.40 10.58 

Fig. 42. — Photographs of Prominences, March 25, 1895 
After Hale 

them, and a few have been observed to attain elevations 
of more than 200,000 miles. Fig. 41 gives specimens of 
both kinds. 

182*. Photography of Prominences. — Quite recently it 
has become possible to photograph these objects at any 
time by utilizing the H and K lines in their spectrum. 
An explanation of the method lies quite beyond our 
scope, but Professor Hale, the director of the new Yerkes 
Observatory, and Deslandres in Paris, have been spe- 
cially successful in this line, and have both constructed 



160 LESSONS IK ASTRONOMY 

spectroscopic apparatus with which, at a single operation, 
they obtain a picture of the entire chromosphere and its 
prominences surrounding an image of the sun itself with its 
spots and faculous regions. The solar image is really only 
a picture of those parts of the disk where the calcium lines 
are bright, and is by no means so perfect a picture as photo- 
graphs made in the usual way ; but it is sufficient to show 
how the prominences stand related to the solar surface, 
and its comparison with an ordinary photograph brings 
out many interesting peculiarities. The new method is a 
great step in the study of solar physics. Fig. 42 is from 
one of Hale's photographs and illustrates well the rapidity 
with which the prominences rise and change their forms. 

183. The Corona. — Probably the most beautiful and 
impressive of all natural phenomena is the corona, the 
" glory " of light which surrounds the sun at a total 
eclipse. The portion of it near the sun is dazzlingly bright 
and of a pearly luster, contrasting beautifully with the 
scarlet prominences, which stud it like rubies. It seems 
to be mainly composed of projecting filaments of light, 
which near the sun are pretty well defined, but at a little 
distance fade out and melt into the general radiance. 
Near the poles of the sun the corona does not usually 
extend very far and has a pretty definite outline, but in 
the spot regions and near the sun's equator faint streams 
sometimes extend to a distance of several degrees; and at 
the distance of the sun every degree means more than a 
million and a half of miles. 

A very striking and perplexing feature is the existence 
of dark rays or rifts, which reach clear down to the very 
edge of the sun. 



THE CORONA 161 

The corona varies greatly in brightness at different 
eclipses, according to the apparent diameter of the moon 
at the time. The portion of the corona nearest the sun 
is so much brighter than the outer regions that a little 
increase of the moon's diameter cuts off a very large pro- 
portion of the light. The total light of the corona is 
usually at least two or three times as great as that of the 
full moon. Fig. 43 is from a photograph of the eclipse 




Fig. 43. — Corona of Eclipse of 1900, Wadesboro, N.C. 

of May, 1900, made at Wadesboro, N.C. At that time 
the sun-spots were at their minimum, and, as is then 
usual, the equatorial " wings " were very long and the 
polar streamers especially numerous and well defined. 

184. Spectrum of the Corona. — A characteristic feature 
of its spectrum is a bright green line. This line was at 
first, and for a long time, supposed to coincide with the 
" 1474 " line of Kirchhoff's map of the spectrum — a very 
puzzling circumstance, as that line is due to iron, and iron 



162 LESSONS m ASTRONOMY 

vapor seemed to be a very improbable substance to be 
found at such an elevation above the hydrogen of the 
chromosphere. Photographs of the corona spectrum made 
in 1896 and at the later eclipses have, however, shown 
that the supposed coincidence with 1474 was a mistake, 
the corona line being slightly more refrangible and nearer 
the blue end of the spectrum. The photographs have 
also detected several other lines in the violet and ultra- 
violet, and it is now clear that the green line and the 
others are due to some still unknown gaseous element 
(probably lighter than hydrogen), which has been provi- 
sionally called coronium, after the analogy of helium. It is 
to be hoped that before very long this substance also may 
be " run to earth " as helium has been. 

185. The corona is proved to be a true appendage of 
the sun, and not, as has been at times supposed, a mere 
optical phenomenon, nor one due to the atmosphere of the 
earth or moon, by two established facts : 

1st. That its spectrum is not that of reflected sunlight, 
but of a self-luminous gas ; and 

2d. Because photographs of the corona, made at widely 
different stations along the track of an eclipse, agree closely 
in details. 

Its real nature and relation to the sun are very difficult 
to explain. It is a gaseous envelope, at least largely gas- 
eous, for it may, and probably does, contain much " dust " 
and " fog." It does not, however, stand in any such rela- 
tion to the globe below as does our atmosphere, since its 
streamers strongly indicate that it is not in equilibrium 
under the sun's attraction, but is largely maintained and 
shaped by powerful repulsive forces. 



THE SUN'S LIGHT 163 

Its phenomena are not yet satisfactorily explained, and 
remind us far more of auroral streamers and of comets' 
tails than of anything that occurs in the lower regions of 
the earth's atmosphere. (See, however, Sec. 306.) 

Its material is of excessive rarity, as is shown by the 
fact that in a number of cases comets have passed directly 
through it (as, for instance, in 1882) without the slightest 
perceptible disturbance. Its density, therefore, must be 
almost inconceivably less than that of the best air-pump 
vacuum which we are able to produce. 

THE SUN'S LIGHT AND HEAT 

186. The Sun's Light. — By photometric measures, which 
we cannot explain here, it is found that the sun gives us 
about 1575 billions of billions (1575 followed by 24 ciphers) 
times as much light as a standard candle * would do at 
that distance. 

The amount of light received from the sun is about 
600,000 times that given by the full moon, about 
7000,000000 times that of Sirius, the brightest of the 
fixed stars, and fully 200000,000000 times that of the 
Pole-star. 

As to the intensity of sunlight, or the intrinsic brightness 
of the sun's surface, we find that it is about 190,000 
times as bright as that of the candle flame, and fully 
150 times as bright as the lime of a calcium light; so 
that even the darkest part of a sun-spot outshines the 

1 The standard candle is a sperm candle weighing one-sixth of a pound 
and burning 120 grains an hour. An ordinary gas-burner usually gives a 
light equivalent to from ten to fifteen candles. 



164 LESSONS IN ASTRONOMY 

lime light. The brightest part of an electric arc-light 
comes nearer sunlight in intensity than anything else we 
know of, being from one-half to one-quarter as bright as 
the solar surface itself. 

The sun's disk is brightest near the center, but the 
variation is slight until we get pretty near the edge, where 
the light falls off rapidly. Just at the sun's limb, the 
brightness is not much more than a third as great as at the 
center. The color there is modified also, becoming a sort 
of orange red. This darkening and change of color are 
due to the general absorption of light by the lower por- 
tions of the sun's atmosphere. According to Langley, if 
this atmosphere were suddenly removed the surface would 
shine out somewhere from two to five times as brightly as 
now, and its tint would become strongly blue, like the 
color of an electric arc. 

187. The Quantity of Solar Heat ; the Solar Constant. — 
The "solar constant" is the number of heat-units which a 
square unit of the earth's surface, unprotected by any 
atmosphere and squarely exposed to the sun's rays, would 
receive from the sun in a unit of time. The heat-unit 
most used at present is the Calory} which is the quantity 
of heat required to raise the temperature of one kilogram 
of water 1° 0. ; and as the result of the best observations 
thus far made (Langley's) it appears that the Solar Constant 
is approximately 80 of these calories to a square meter in 
one minute. At the earth's surface a square meter, 
owing to the absorption of a large percentage of heat by 

1 A u small calory " is also used, one-thousandth as large as this : viz., 
the quantity of heat which will raise the temperature of one gram of 
water 1° C. It might be called the Calorette. 



THE SOLAR CONSTANT 165 

the air, would, however, seldom actually receive more than 
from ten to fifteen calories in a minute. 

The true value of the solar constant is still uncertain by 
a very large percentage, different observers giving values 
all the way from 20 to 40. 

The method of determining the solar constant is simple, 
so far as the principle goes, but the practical difficulties 
are serious, and thus far have prevented our obtaining the 
accuracy desirable. The determination is made by allowing 
a beam of sunlight of known diameter to fall upon a known 
quantity of water for a known time, and measuring how 
much the water rises in temperature. The principal diffi- 
culty lies in determining the proper allowance to be made 
for absorption of the sun's heat in passing through the 
air, since this absorption varies continually and to a great 
extent with changing conditions. Besides this it is neces- 
sary to measure and allow for the heat which is received 
by the water during the experiment from other sources 
than the sun. 

188. Solar Heat at the Earth's Surface. — Since it 
requires about 80 calories of heat to melt one kilogram of 
ice, it follows that, taking the solar constant at 30, the 
heat received from the sun when overhead would melt in 
an hour a sheet of ice about -A of an inch thick. From 
this it is easily computed that the amount of heat received 
by the earth from the sun in a year would melt a shell of 
ice 177 feet thick all over the earth's surface. 

" Solar engines " have been constructed within the last 
few years, in which the heat received upon a large reflector 
is made to evaporate water in a suitable boiler, and to drive 
a steam engine. It is found that the heat received upon a 



166 LESSONS IX ASTRONOMY 

reflector ton feet square can be made to give practically 

about one horse-power. 

189. Radiation from the Sun's Surface. — If we attempt 
to estimate the intensity of the radiation from the surface of 
the sun itself, we reach results which are simply amazing. 
We must multiply the solar constant observed at the earth 
by the square o( the ratio between the earth's distance 
from the sun and the distance of the sun's surface from 
its own center, i.e.. by the square of (*-!$$$j{-*)i or about 
46,000 : in other words, the amount of heat emitted in a 
minute by a square foot of the sun's surface is about 
46,000 times as great as that received by a square foot of 
surface at the distance of the earth. Carrying out the 
figures, we find that, if the sun were frozen over com- 
pletely to a depth of about 64 feet, the heat it emits would 
be sufficient to melt the iee in one minute : that if a 
bridge of iee could be formed from the earth to the sun 
by an iee column "2} miles square, and if in some way the 
entire solar radiation could be concentrated upon it, it 
would be melted in one second, and in seven more would 
be dissipated in vapor. 

Expressing it in terms of energy, we find that the solar 
radiation is more than 130,000 horse-power continuously 
for each square meter of the sun's surface. 

So far as we can now see. only a very small traction of this whole 

radiation ever roaches a resting place. The earth intercepts about 

. and the other planets of the solar system receive in 

all perhaps from ten to twenty times as much. Something like 

seems to be utilized within the limits of the solar system. 

190. The Sun's Temperature. — We can determine with 
some accuracy the amount of heat which the sun gives: 



THE SUN'S TEMPERATURE 167 

to find its temperature is a very different thing, and we 
really have very little knowledge about it, except that it 
must be extremely high, — far higher than that of any 
terrestrial source of heat now known. The difficulty is 
that our laboratory experiments do not give the necessary 
data from which we can determine what temperature sub- 
stances like those of which the sun is composed must have, 
in order to enable them to send out heat at the rate which 
we observe. Of two bodies at precisely the same tempera- 
ture, one may send out heat a hundred times more rapidly 
than the other. 

The estimates as to the temperature of the photosphere 
run all the way from the very low ones of some of the 
French physicists (who set it at about 2500° C.) to the 
absurd values of Secchi and Ericsson, who put the figure 
among the millions. The latest and most authoritative 
determinations by Wilson and Gray in Ireland make it 
about 7000° C, or 12,500° F. The highest terrestrial 
temperature (attained in the electric arc) is about 4000° C. 

A very impressive demonstration of the intensity of the. 
sun's heat is found in the fact that in the focus of a 
powerful burning lens all known substances melt and 
vaporize ; and yet it can be shown that at the focus of the 
lens the temperature can never even nearly equal that of 
the source from which the heat is derived. 

191. Constancy of the Sun's Heat. — It is still a question 
whether the total amount of the sun's radiation does or 
does not vary from time to time. There may be consider- 
able fluctuations in the hourly or daily quantity of heat 
without our being able to detect them with our present 
means of observation. 



168 LESSONS IN ASTRONOMY 

As to any steady progressive increase or decrease in the 
amount of heat received from the sun, it is quite certain 
that no considerable change has occurred for the past two 
thousand years, because the distribution of plants and 
animals on the earth's surface is practically the same as in 
the earliest days of history. It is, however, rather prob- 
able than otherwise that the great changes of climate, which 
Geology indicates as having formerly taken place on the 
earth, may ultimately be traced to changes in the condition 
of the sun. 

192. Maintenance of the Solar Heat. — We cannot here 
discuss the subject fully, but must content ourselves with 
saying, — 

First, negatively, that this maintenance cannot be 
accounted for on the supposition that the sun is a hot 
body, solid or liquid, simply cooling , nor by combustion, 
nor (adequately) by the fall of meteors on the sun's sur- 
face, though this cause undoubtedly operates to a limited 
extent. 

Second, we can say positively, that the solar radiation can 
be accounted for on the hypothesis first proposed by Helm- 
holtz, that the sun is mainly gaseous, and shrinking slowly 
but continuously. While we cannot see any such shrink- 
age, because it is too slow, it is a matter of demonstration 
that if the sun's diameter should contract about 300 feet 
a year, heat enough would be generated to keep up its radi- 
ation without any lowering of its temperature. If the 
shrinkage were more than this, the sun would be hotter at 
the end of the year than it was at the beginning. 

We can only say that while no other theory meets the 
conditions of the problem, this appears to do so perfectly, 



AGE AXJ) DURATION OF SUN 169 

and therefore has probability in its favor. It seems to be 
only a continuation of the process of condensation by 
which the sun itself and the solar system have been 
formed from the original cloud or nebula. 

193. Age and Duration of the Sun. — Of course if this 
theory is correct, the sun's heat must ultimately come to 
an end ; and looking backward, it must have had a begin- 
ning. If the sun keeps up its present rate of radiation, 
it must, on this hypothesis, shrink to about half its diam- 
eter in some 5,000000 years at the longest. It will then be 
eight times as dense as now, and can hardly continue to be 
mainly gaseous, so that the temperature must begin to fall 
quite sensibly. It is not, therefore, likely, in the opinion 
of Professor Newcomb, that the sun will continue to give 
heat sufficient to support the present conditions upon the 
earth for much more than 10,000000 years, if so long. 

On the other hand, it is certain that the shrinkage of the 
sun to its present dimensions from a diameter larger than 
that of the orbit of Neptune, the remotest of the planets, 
would produce about 18,000000 times as much heat as 
the sun now throws out in a year. Hence, if the sun's heat 
has been, and still is, wholly due to the contraction of its 
mass, it cannot have been emitting heat at the present rate, 
on this shrinkage hypothesis, for more than 18,000000 
years. But notice the "if." It is quite possible that the 
solar system may have received in the past supplies of 
heat other than that due to the contraction of the sun's 
mass. If so, it may be much older. 

194. Constitution of the Sun. — To sum up : the received 
opinion is that the sun is mainly composed of the same 
chemical elements as the earth, but that in the body, or 



170 LESSONS IN ASTRONOMY 

nucleus, of the sun the heat is so tremendous that they are 
all in the state of vapor or gas in spite of the great pressure 
to which they are subjected. 

The photosphere is probably a sheet of luminous clouds, 
constituted mechanically like terrestrial clouds, i.e., of 
small, solid, or liquid particles, very likely of carbon, 
floating in gas. 

These photospheric clouds float in an atmosphere com- 
posed of those gases which do not condense into solid or 
liquid particles at the temperature of the solar surface. 
This atmosphere is laden, of course, with the vapors out 
of which the clouds have been condensed, and constitutes 
the reversing lager which produces the dark lines of the 
solar spectrum. 

The chromosphere and prominences appear to be com- 
posed of permanent gases, mainly hydrogen and helium, 
which are mingled with the vapors in the region of the 
photosphere, but rise to far greater elevations. For the 
most part the prominences appear to be formed by jets of 
hydrogen and helium, ascending through the interstices 
between the photospheric clouds, like flames playing over 
a coal fire. 

As to the corona, it is as yet impossible to give any 
satisfactory explanation of all the phenomena that it pre- 
sents, and since thus far it has been possible to observe it 
only during the brief moments of total eclipses, progress 
in its study has been necessarily slow. 



CHAPTER VII 

ECLIPSES AND THE TIDES 

Form and Dimensions of Shadows — Eclipses of the Moon — Solar Eclipses — 
Total, Annular, and Partial — Number of Eclipses in a Year — Recurrence 
of Eclipses and the Saros — Occupations — The Tides 

195. Occasionally the sun or moon is for a short time 
obscured by an Eclipse (literally, a "swoon"). Solar 
eclipses, when total, are among the most impressive phe- 
nomena in the range of human experience, and find place 
all along the records of authentic history. To the super- 
stitious and ignorant they have always been terrifying and 
portentous; but to the astronomer wonderfully beautiful 
— golden opportunities for observations important and 
otherwise impossible. 

An eclipse of the moon is caused by its passing through 
the shadow of the earth; an eclipse of the sun by the 
moon's passing between the sun and the observer, or, what 
comes to the same thing, by the passage of the moon's 
shadow over the observer. 

The " shadow," in Astronomy, is the space from which 
sunlight is excluded by an intervening body ; speaking 
geometrically, it is a solid, not a surface. Since the sun 
and the other heavenly bodies are very nearly spherical, these 
shadows are cones with their axes in the line which joins the 
centers of the sun and the shadow-casting body, the point 
being always directed away from the sun. 

171 



172 LESSONS m ASTRONOMY 

ECLIPSES OF THE MOON 

196. Dimensions of the Earth's Shadow. — The length 
of the shadow is easily found. In Fig. 44 is the center 
of the sun and E the center of the earth, and aCb is the 
shadow of the earth cast by the sun. It is readily shown 
by Geometry that if we call EC, the length of the shadow, 
Z, and OE, the distance of the earth from the sun, D, then 

L = D X f — j ' R being OA, the radius of the sun, and r 

being Ea, the radius of the earth. Putting in the values of 



Fig. 44. — The Earth's Shadow 



R and r from Sees. 160 and 112 (where, however, the earth's 
mean diameter is given instead of radius) the fraction, 

f — ] j comes out nearly ttttTt I and multiplying this 

by D (93,000000), we get 857,000 miles for the average 
length of the earth's shadow. 

The length varies about 14,000 miles on each side of 
the mean, in consequence of the variation of the earth's 
distance from the sun at different times of the year. 

From the cone aCb all sunlight is excluded, or would be were it 
not for the fact that the atmosphere of the earth bends some of the 



LUNAR ECLIPSES 173 

rays which pass near the earth's surface into its shadow. The effect 
of this atmospheric refraction is to increase the apparent diameter 
of the shadow about two per cent, but to make it less perfectly dark. 

If we draw the lines Be and Ad, crossing at P, between 
the earth and the sun, they will bound the penumbra, 
within which a part, but not the whole, of the sunlight is 
cut off ; an observer outside of the shadow, but within this 
partly shaded space, would see the earth as a black body 
encroaching on the sun's disk, though not covering it. 

197. Lunar Eclipses. — The axis, or central line, of the 
earth's shadow is always directed to a point directly oppo- 
site the sun. If, then, at the time of full moon, the moon 
happens to be near the ecliptic, i.e., not far from one of 
the nodes (the points where her orbit cuts the ecliptic), 
she will pass through the shadow and be eclipsed. Since, 
however, the moon's orbit is inclined 5° 8' to the ecliptic, 
lunar eclipses do not happen very frequently, — seldom more 
than twice a year, because the moon at the full usually 
passes north or south of the shadow, without touching it. 

Lunar eclipses are of two kinds, partial and total : total 
when she passes completely into the shadow ; partial when 
she only partly enters it, going so far to the north or south 
of the center that only a portion of the disk is obscured. 
An eclipse of the moon when central (i.e., when the moon 
crosses the center of the shadow) may continue total for 
about two hours, the interval from the first to the last 
contact being about two hours more. This depends upon 
the facts that the moon's hourly motion is nearly equal to 
its own diameter, and that the diameter of the earth's 
shadow where the moon crosses it is between two and 
three times the diameter of the moon itself. The duration 



174 LESSONS m ASTKONOMY 

of an eclipse that is not central varies of course with the 
part of the shadow traversed by the moon. 

198. Phenomena of Total Eclipses of the Moon. — Half 
an hour or so before the moon reaches the shadow, its edge 
begins to be sensibly darkened by the penumbra, and the 
edge of the shadow itself, when it first touches the moon, 
appears nearly black by contrast with the bright parts of 
the moon's surface. To the naked eye the outline of the 
shadow looks fairly sharp ; but even with a small telescope 
it appears indefinite, and with a large telescope of high 
magnifying power the edge of the shadow becomes entirely 

Fig. 45. — Light bent into Earth's Shadow by Refraction 

indistinguishable, so that it is impossible to determine 
within half a minute or so the time when it reaches any 
particular point. 

After the moon has wholly entered the shadow, her disk 
is usually distinctly visible, illuminated with- a dull, copper- 
colored light, which is sunlight, deflected around the earth 
into the shadow by the refraction of our atmosphere, as 
illustrated by Fig. 45. The brightness of the moon's disk 
during a total eclipse of the moon differs greatly at dif- 
ferent times, according to the condition of the weather on 
the parts of the earth which happen to lie at the edges of 
the earth's disk as seen from the moon. If it is cloudy 
and stormy there, little light will reach the moon ; if it 
happens to be clear, the quantity of light deflected into 



DIMENSIONS OF MOON'S SHADOW 175 

the shadow may be very considerable. In the lunar eclipse 
of 1884, the moon was for a time absolutely invisible to 
the naked eye, — a very unusual circumstance. 

During the eclipse of JaD. 28, 1888, although the moon was 
pretty bright to the eye, Pickering found that its photographic power, 
when centrally eclipsed, was only about t^-Jooo °f what it had been 
before the shadow covered it. 

199. Computation of a Lunar Eclipse. — The computation of a 
lunar eclipse is not at all complicated, though we do not propose to 
enter into it. Since all its phases are seen everywhere at the same 
absolute instant wherever the moon is above the horizon, it follows 
that a single calculation giving the Greenwich times of the different 
phenomena is all that is needed. Such computations are made and 
published in the Nautical Almanac. The observer needs only to cor- 
rect the predicted time by simply adding or subtracting his longitude 
from Greenwich, in order to get the true local time. With an eclipse 
of the sun the case is very different. 



ECLIPSES OF THE SUN 

200. The Length of the Moon's Shadow is very nearly 
^1-q of its distance from the sun, and averages 232,150 
miles. It varies not quite 7800 miles, ranging from 
228,300 to 236,050. 

Since the mean length of the shadow is less than the 
mean distance from the earth (238,800 miles), it is evident 
that on the average the shadow will fall short of the earth. 
The eccentricity of the moon's orbit, however, is so great 
that she is sometimes more than 31,000 miles nearer than 
at others. If when the moon is nearest the earth, the 
shadow happens to have at the same time its greatest pos- 
sible length, its point may reach nearly 18,400 miles beyond 



176 



LESSONS m ASTRONOMY 



the earth's surface. In this case the cross-section of the 
shadow where the earth's surface cuts it (at o in Fig. 46) 
will be about 168 miles in diameter, which is the largest 
value possible. On the other hand, when the moon is 
farthest from the earth, we may have the state of things 
indicated by placing the earth at B in Fig. 44. The ver- 
tex of the shadow, F, will then fall about 21,000 miles short 
of the earth's surface, and the cross-section of the shadow 
produced will have a diameter of 196 miles at o\ where 
the earth's surface cuts it. 

201. Total and Annular Eclipses. — To an observer within 
the shadow cone (i.e., between V and the moon, Fig. 46) 
the sun will be totally eclipsed. An observer in the 




— > To Sun 
Fig. 46. — The Moon's Shadow on the Earth 

"produced" cone beyond Fwill see the moon apparently 
smaller than the sun, leaving a ring of the sun uneclipsed ; 
this is what is called an annular eclipse. These annular 
eclipses are considerably more frequent than the total, and 
now and then an eclipse is annular in part of its course 
across the earth and total in part. This is when the point 
of the moon's shadow extends beyond the surface of the 
earth, but does not reach as far as its center. 

The track of the eclipse across the earth will, of course, be 
a narrow stripe having its width equal to the cross-section 
of the shadow, and extending across the hemisphere which 
is turned towards the moon at the time, though not 



PENUMBRA AND PARTIAL ECLIPSES 177 

necessarily passing the center of that hemisphere. Its 
course is always from the west towards the east, but 
usually considerably inclined towards the north or south. 

202. The Penumbra and Partial Eclipses. — The penumbra 
can easily be shown to have a diameter on the line CD 
(Fig. 46) a little more than twice the diameter of the moon, 
or over 4000 miles. An observer situated within this 
penumbra has a partial eclipse. If he is near to the cone 
of the shadow, the sun will be mostly covered by the moon ; 
if near the outer edge of the penumbra, the moon will but 
slightly encroach on the sun's disk. While, therefore, a 
total or annular eclipse is visible as such only by observers 
within the narrow path traversed by the shadow-spot, the 
same eclipse will be visible as a partial one anywhere within 
2000 miles on each side of the path; and the 2000 miles 
must be reckoned square to the axis of the shadow, and 
may correspond to a much greater distance upon the 
spherical surface of the earth. 

203. Velocity of the Shadow and Duration of an Eclipse. — 
Were it not for the earth's rotation, the moon's shadow 
would pass the observer at the rate of about 2100 miles an 
hour. The earth, however, is rotating towards the east in 
the same general direction as that in which the shadow 
moves, so that the relative velocity is usually much less. 

A total eclipse of the sun observed at a station near the 
equator, under the most favorable conditions possible, may 
continue total for about 7 m 58 s . In latitude 40° the duration 
can barely equal 6 m 15 s . 

An annular eclipse may last at the equator for 12 m 24 s , 
the maximum width of the ring of the sun visible around 
the moon being 1' 37". 



ITS LESSONS IN ASTRONOMY 

In the observation of an eclipse, tour contacts arc recognized: the 
Jtrsi when the edge of the moon tirst touches the edge of the sun. 

the second when the eclipse becomes total or annular, the thi\ 
the cessation of the total or annular phase, and the fourth when the 

moon finally leaves the solar disk. From the tirst contact to the 
fourth the time may he a little over four hours. In a partial eclipse, 
only the tirst and fourth are observable, and the interval between them 
may be very small when the moon just grazes the edge of the sun. 

The magnitude of an eclipse is usually reckoned in aioits, the 
digit being .'- of the sun's diameter. An eclipse of nine digits is 
one in which the disk of the moon covers three-fourths of the sun's 
diameter at the middle of the eclipse. 

204. Phenomena of a Solar Eclipse. - There is nothing 
of special interest until tho sun is mostly covered, though 
before that time the shadows oast by tho foliage begin to bo 
peculiar. 

The light shining through every small interstice among the leaves, 
instead of forming as usual a circle on the ground, makes a little 
>eont. — an image of the partly covered sun. 

About ton minutes before totality the darkness begins to 

be felt, and tho remaining light, coming, as it does, from tho 
edge of the sun, is not only faint but yellowish, more like 
that of a calcium light than sunshine. Animals are per- 
plexed, and birds go to roost. The temperature falls, and 
dew appears. In a few moments, if the observer is so situ- 
ated that his view commands the distant western horizon, 
the moon's shadow is seen coming, much like a heavy 
thunder-shower, and advancing with almost terrifying 
swiftness. As soon as the shadow arrives, and sometimes 
a little before, the corona and prominences become visible, 
while the brighter planets and stars of the tirst three 
magnitudes make their appearance. 



FREQUENCY OF ECLIPSES 179 

The suddenness with which the darkness pounces upon 
the observer is startling. The sun is so brilliant that even 
the small portion which remains visible up to the moment 
of total obscuration so dazzles the eye that it is unprepared 
for the sudden transition. In a few moments, however, the 
eye adjusts itself, and it is found that the darkness is really 
not very intense. If the totality is of short duration, say 
not more than two minutes, there is not much difficulty in 
reading an ordinary watch face. In an eclipse of long 
duration (four or five minutes) it is much darker, and 
lanterns become necessary. 

205. Calculation of a Solar Eclipse. — A solar eclipse cannot be 
dealt with in any such summary way as a lunar eclipse, because the 
absolute times of contact are different at every different station. The 
path which the shadow of a total eclipse will describe upon the earth 
is roughly mapped out in the Xautical Almanacs several years before- 
hand, and with the chart are published the data necessary to enable 
one to calculate with accuracy the phenomena for any given place ; 
but the computation is rather long and somewhat complicated. 

Th. Oppolzer. a Viennese astronomer, published some years ago a 
remarkable book entitled " The Canon of Eclipses," containing the 
elements of all eclipses (8000 solar and 5200 lunar) occurring between 
the year 1207 B.C. and a.d. 2162, with maps showing the approximate 
tracks of all the solar eclipses. 

206. Frequency of Eclipses and Number in a Year. — The 
least possible number in a year is two, both of the sun; the 
largest seven, five solar and two lunar or four solar and 
three lunar; the most usual number is four. 

The eclipses of a given year always take place at two 
opposite seasons, which may be called the eclipse months 
of the year, near the times when the sun crosses the nodes of 
the moon's orbit. Since the nodes move westward around 



180 LESSONS IN ASTRONOMY 

the ecliptic once in about nineteen years (Sec. 134), the 
time occupied by the sun in passing from a node to the 
same node again is only 346.62 days, which is sometimes 
called the eclipse year. 

Taking the whole earth into account, the solar eclipses 
are the more numerous, nearly in the ratio of 3 : 2. It is 
not so, however, with those which are visible at a given place. 
A solar eclipse can be seen only by persons who happen 
to be on the narrow track described by the moon's shadow 
in its passage across the globe, while a lunar eclipse is 
visible over considerably more than half the earth, — either 
at its beginning or end, if not throughout its whole duration. 
This more than reverses the proportion, i.e., at any given 
place lunar eclipses are considerably more frequent than 
solar. Solar eclipses that are total somewhere or other on 
the earth's surface are not very rare, averaging about one for 
every year and a half. But at any given place a total eclipse 
happens only once in about 360 years in the long run. 

During the 19th century seven shadow tracks crossed the United 
States, the last in May, 1000. During the 20th the same number 
are predicted, — the next in 1918, the track of which runs from 
Oregon to Florida. (Our insular possessions are not included in 
this reckoning.) 

207. Recurrence of Eclipses ; the Saros. — It was known 
to the Egyptians, even in prehistoric times, that eclipses 
occur at regular intervals of 18 years and 11J days (10J 
days, if there happen to be five leap years in the interval). 
They named this period the Saros. It consists of 223 syn- 
odic months, containing 6585.32 days, while 19 eclipse years 
contain 6585.78. The difference is only about 11 hours, in 
which time the sun moves on the ecliptic about 28'. 



CAUSE OF THE TIDES 181 

If, therefore, a solar eclipse should occur to-day with 
the sun exactly at one of the moon's nodes, at the end of 
223 months the new moon will find the sun again close to 
the node (only 28' west of it), and a very similar eclipse 
will occur again ; but the track of this new eclipse will lie 
about 8 hours of longitude farther went on the earth, on 
account of the odd 1 :; (l " (l of a day in the Saros. The usual 
number of eclipses in a Saros is a little over 70, varying 
two or three one way or the other. 

In the Saros closing Dec. 22, 1889, the total number was 72, — 
29 lunar and 13 solar. Of the latter, 29 were central (13 total, 10 
annular), and 14 were only partial. 

THE TIDES 

208. Cause of the Tides. — Since the tides depend upon 
the action of the sun and of the moon upon the waters of 
the earth, they may properly 
he considered here before we 
deal with the planetary sys- 
tem. We do not propose to 
go into the mathematical 
theory of the phenomena at 
all, as it lies far beyond our 
limitations ; but any person 
can see that a liquid globe falling freely towards an attract- 
ing body, which attracts the nearer portions more powerfully 
than the more remote, will be drawn out into an elongated 
lemon-shaped form, as illustrated in Fig. 47, and if the 
globe, instead of being liquid, be mainly solid, but has 
large quantities of liquid on its surface, substantially the 




The Tides 



182 LESSONS m ASTRONOMY 

same result will follow. Now the earth is free in space, and 
though it has other motions, it is also falling towards the 
moon and towards the sun, and is affected precisely as it 
would be if its other motions did not exist. The conse- 
quence is that at any time there is a tendency to elongate 
those diameters of the earth which are pointed towards the 
moon and towards the sun. The sun is so much farther 
away than the moon that its effect in thus deforming the 
surface of the earth is only about five-elevenths as great 
as that of the moon. 

209. The tides consist in a regular rise and fall of the ocean 
surface, the average interval between corresponding high 
waters on successive days at any given place being 24 h 51 m , 
which is precisely the same as the average interval between 
two successive passages of the moon across the meridian ; 
and since this coincidence is maintained indefinitely, it of 
itself makes it certain that there must be some causal con- 
nection between the moon and the tides. Some one has said 
that the odd fifty-one minutes is the moon's " earmark." 

That the moon is largely responsible for the tides is also 
shown by the fact that when the moon is in perigee, at the 
nearest point to the earth, the tides are nearly twenty per 
cent higher than when she is in apogee. 
y 210. Definitions. — While the water is rising, it is flood- 
tide ; while falling, it is ebb-tide. It is high water at the 
moment when the water-level is highest, and low water 
when it is lowest. The spring-tides are the largest tides 
of the month, which occur near the times of new and full 
moon, while the neap tides are the smallest, and occur at 
half-moon, the relative heights of spring and neap tides 
being about as 8 : 3 (11 + 5 : 11 - 5). 



MOTION OF THE TIDES 183 

At the time of the spring-tides, the interval between 
the corresponding tides of successive days is less than the 
average, being only about 24 h 3 m 8 (instead of 24 h 51 m ), and 
then the tides are said to prime. At the neap tides the 
interval is greater than the mean, — about 25 h 6 m , — and 
the tide lags. 

The establishment of a port is the mean interval between 
the time of high water at that port and the next preceding 
passage of the moon across the meridian. The " establish- 
ment" of New York, for instance, is 8 h 13 m . The actual 
interval between the moon's transit and high water varies, 
however, nearly half an hour on each side of this mean 
value at different times of the month, and under varying 
conditions of the weather. 

211. Motion of the Tides. — If the earth were wholly 
composed of water, and if it kept always the same face 
towards the moon, as the moon does towards the earth, 
then (leaving out of account the sun's action for the 
present) a permanent tide would be raised upon the earth, 
as indicated in Fig. 47. The difference between the water- 
level at A and D would be a little less than two feet. 

Suppose, now, the earth put in rotation. It is evident 
that the two tidal waves A and B would move over the 
earth's surface, following the moon at a certain angle 
dependent on the inertia of the water, and tending to 
move with a westward velocity equal to the earth's east- 
ward rotation, — about 1000 miles an hour at the equator. 
The sun's action would produce similar tides superposed 
upon the moon's tide, and about two-fifths as large ; and 
at different times of the month these two pairs of tides 
would sometimes conspire and sometimes be opposed. 



184 LESSONS IN ASTRONOMY 

If the earth were entirely covered with deep water, then, 
according to Professor Darwin, and considering only the 
lunar tide, the tide-waves would run around the globe 
regularly, and if the depth of the water were not less than 
14 miles, the two tide crests would keep on the line joining 
the centers of the moon and earth. 

If the depth were somewhat less, the tide crests on the 
equator would follow the moon at an angle of 90°, but in 
the high latitudes they would still move as in the deeper 
ocean, while in some intermediate latitude there would 
be a belt of eddying currents without either rise or fall. 

But the varying depth of the ocean in different regions 
and the irregular contour of its shore-line greatly compli- 
cate the problem. Moreover, the continents of North and 
South America, with the southern Antarctic continent, 
make a barrier almost from pole to pole, leaving only a 
narrow passage at Cape Horn. 

As a consequence it is quite impossible to determine by 
theory what the course and character of tide-waves must 
be. We have to depend upon observations, and observa- 
tions are more or less inadequate, because, with the excep- 
tion of a few islands, our only possible tide stations are 
on the shores of continents where local circumstances 
largely control the phenomena. 

212. Free and Forced Oscillations. — If the water of the 
ocean is suddenly disturbed, as, for instance, by an earth- 
quake, and then left to itself, a " free wave " is formed, 
which, if the horizontal dimensions of the wave are large 
as compared with the depth of the water (i.e., if it is many 
hundred miles in length), will travel at a rate which depends 
simply on the depth of the water. 



COUKSE OF THE TIDE-WAVE 185 

Its velocity is equal, as can be proved, to the velocity acquired by 
a body in falling through half the depth of the ocean. Observations 
upon waves caused by certain earthquakes in South America and 
Japan have thus informed us that between the coasts of those 
countries the Pacific averages between 2J and 3 miles in depth. 

Now, as the moon in its apparent diurnal motion passes 
across the American continent each day and comes over 
the Pacific Ocean, it starts such a "parent" wave in the 
Pacific, and a second one is produced twelve hours later. 
And in the same manner the sun, of course, also starts its 
own independent smaller tide-waves. 

These waves, once started, move on nearly (but not 
exactly) like a free earthquake wave — not exactly, because 
the velocity of the earth's rotation being about 1040 miles 
at the equator, the moon moves (relatively) westward 
faster than the wave can naturally follow it, and so for 
a while the moon slightly accelerates the wave. The tidal 
wave is thus, in its origin, a "forced oscillation"; in its 
subsequent travel it is very nearly, but not entirely, " free." 

Of course as the moon passes on over the Indian and 
Atlantic oceans, it starts waves in them also, which com- 
bine with the parent wave coming in from the Pacific. 

213. Course of Travel of the Tide- Wave. — The parent wave 
appears to start twice a day in the Pacific Ocean, off Callao, on the 
coast of South America. From this point the wave travels northwest 
through the deep water of the Pacific at the rate of about 850 miles 
an hour, reaching Kamchatka in ten hours. Through the shallow 
water to the west and southwest the velocity is only from 400 to 600 
miles an hour, so that the wave is six hours old when it reaches New 
Zealand. Passing on by Australia and combining with the small 
wave which the moon starts in the Indian Ocean, the resultant tide 
crest reaches the Cape of Good Hope in about twenty-nine hours and 



L86 



LESSONS IN ANTU.ONOMY 



cuicrs bhe Atlantic Here it combines with a smaller tide-wave, 
bwelve hours younger, which has "backed" into the Atlantic around 
Cape Horn, and It is also modified by bhe direct bide produced by bhe 
moon and sun in (he Atlantic. The tide resulting from bhe com- 
bination of Mic.sc waves then travels northward bhrough bhe Atlantic 
at bhe rate of about Too miles an hour. It, is about forty hours old 

when it first reaches the coast of the United States in Florida; and 

our coast Lies in such a direction that it arrives at all bhe prinoipal 

ports within two or three hours of the same time. It is forty-one or 
forty-two hours old when it reaches New York and Boston. 

To reach London it has to travel around the northern end of 
Scotland and through the North Sea,, and is nearly sixty hours old 
when it arrives at (hat port. 

In the great oceans there are three or four such fide crests, follow 
\\\ X nearly in the same track, hut with continual minor changes. 

214. Height of the Tides. In mid ocean (lie difference 
between high and low water is usually between (wo and 




Q l> F S K 

Km. 48. — Increase in Height Of Tide cm approaching the Shore 



three foot, as observed on isolated islands in the deep water. 
On the continental shores the height is ordinarily much 
greater. As soon as the tide-wave " touches bottom," so 
to speak, the velocity is diminished, the tide crests are 
crowded more closely together, and the height of the tide 
is very much increased, as indicated in Fig, 48. 



Theoretically, it varies inversely as the fourth root of the depth; 

i.r., where the water is 1(H) feet deep the tide-wave should he twice 
as high as at (he depth of L600 feci, 



TIDES IX R1VEKS 187 

Where the configuration of the shore forces the t.ido into 
a corner it sometimes rises very high. At Minns Basing on 
the Bay of Fundy, tides of TO feet are reported as not 
uncommon, and an altitude of 100 feet is said to occur 
sometimes. At Bristol in the English Channel, tides of 
40 or 50 feet are reached ; at the same time, on the coasl 
of Ireland, just opposite, the tide is very small. 

215. Tides in Rivers. — The tide-wave ascends a river at a rate 
which depends upon the depth of the water, the amount of friction, 
and the swiftness of the stream. It may, and generally does, ascend 
until it. comes to a rapid where the velocity of the current is greater 
than that of the wave. In shallow streams, however, it. dies out 
earlier. Contrary to what. Is usually supposed, it often ascends to an 
elevation far above that of the highest crest of the tide-wave at the 
river's mouth. In the La Plata and Amazon, the tide goes up to an 

ation of at least 100 feet above the sea-level. The velocity of a 
tide-wave in a rivo.r seldom exceeds 10 or 20 miles an hour, and is 
ordinarily much le 



CHAPTER VIII 

THE PLANETARY SYSTEM 

The Planets in General — Their Number, Classification, and Arrangement — 
Bode's Law — Their Orbits — Kepler's Laws and Gravitation — Apparent 
Motions and the Systems of Ptolemy and Copernicus — Determination of 
Data relating to the Planets, their Diameter, Mass, etc. — Herschel's Illus- 
tration of the Solar System — Description of the Terrestrial Planets — 
Mercury, Venus, and Mars 

216. The earth is one of a number of bodies called 
Planets, i.e., " wanderers," which revolve around the sun 
in oval orbits that are nearly circular and lie nearly in one 
plane or level. There are eight which are of considerable 
size, besides a group of several hundred minute bodies 
called the " asteroids," which seem to represent in some 
way a ninth planet, either broken to pieces, or somehow 
ruined in the making. 

217. Classification of the Planets. — The four inner 
ones have been called by Humboldt the terrestrial planets, 
because the earth is one of them, and the others resemble it 
in size and density. In the order of distance from the sun 
they are Mercury, Venus, the Earth, and Mars. The four 
outer ones Humboldt calls the major planets, because they 
are much larger and move in larger orbits. They seem 
to be bodies of a different sort from the earth, very much 
less dense and probably of higher temperature. They are 
Jupiter, Saturn, Uranus, and Neptune. 

188 



'Y 



THE PLANETS IN GENERAL 



189 



The asteroids (from the Greek astereidos, i.e., starlike 
planets), called by some minor planets, all lie in the vacant 
space between Mars and Jupiter, and appear to contain in 
the aggregate about as much material as would make a 
planet not so large as Mars. 

All of the planets except Mercury and Venus have 
satellites. The Earth has one, Mars two, Jupiter five, 
Saturn eight (possibly nine), Uranus four, Neptune one, — 
twenty-one in all. 

218. The following little table contains in round num- 
bers the principal numerical facts as to the planets. 



Name 


Distance in 

Astronomical 

Units 


Period 


Diameter 


Mercury 

Venus 

Earth 

Mars 

Asteroids 

Jupiter 

Saturn 

Uranus 

Neptune 


0.4 

0.7 

1.0 

1.5 

3.0 ± 

5.2 

9.5 
10.2 
30.1 


3 months 
7£ months 
1 year 

1 yr. 10 mos. 
3 years to 9 years 
11.9 years 
29.5 " 
84.0 " 
164.8 " 


3000 miles 

7700 " 

7918 " 

4200 " 
500 to 10 miles 
86,000 miles 
73,000 " 
32,000 " ?,- 
35,000 " ? 



This table should be learned by heart. More accurate 
data will be given hereafter, but the round numbers are 
quite sufficient for all ordinary purposes and are much 
more easily remembered. 

219. Bode's Law. — If we set down a row of 4's, to the 
second 4 add 3, to the third 6, to the fourth 12, etc., a 
series of numbers will result which, divided by 10, will 
represent the planetary distances very nearly, except in the 



190 LESSONS IN ASTRONOMY 

case of Neptune, whose distance is only 30 instead of 39, 
as the rule would make it. Thus : 



4 


4 


4 


4 


4 


4 


4 


4 


4 




3 


6 


12 


24 


48 


96 


192 


384 


I 


7 


10 


16 


[28] 


52 


100 


196 


388 


8 


? 


e 


$ 


Q> 


y. 


h 


¥ 


t» 



(The characters below the numbers are the symbols of the 
planets, used in almanacs instead of their names.) 

This law seems to have been first noticed by Titius of Wittenberg, 
but bears the name of Bode, Director of the Observatory of Berlin, 
who first secured general attention to it. 

No logical reason can yet be given for it. It may be a mere con- 
venient coincidence, or it may be the result of the process of develop- 
ment, which brought the solar system into its present state. 

220. Kepler's Laws. — Three famous laws discovered by 
Kepler (1607-1620) govern the motions of the planets. 

I. The orbit of each planet is an ellipse with the sun in 
one of its foci. (For a description of the ellipse, see Appen- 
dix, Sec. 429.) 

II. In the motion of each planet around the sun, the 
radius vector describes equal areas in equal times. (For 
illustration, see Sec. 121, Fig. 14.) 

III. The squares of the periods of the planets are propor- 
tional to the cubes of their mean distances from the sun. This 
is known as the " Harmonic Law." Stated as a propor- 
tion it reads : P x 2 : P 2 2 : : A^ : A£, or in words : 

The square of the period of planet No. 1 is to the square 
of the period of planet No. 2 as the cube of the mean dis- 
tance of planet No. 1 is to the cube of the mean distance of 
planet No. 2. Planets No. 1 and No. 2 are any pair of 



THE PLANETS IN GENERAL 191 

planets selected at pleasure. (For fuller illustration, see 
Appendix, Sec. 430.) 

It was the discovery of this law which so filled Kepler 
with enthusiasm that he wrote, "If God has waited 6000 
years for a discoverer, I can wait as long for a reader." 

221. Gravitation. — When Kepler discovered these three 
laws he could give no reason for them — no more than we 
can now for Bode's law ; — but some sixty years later 
Newton showed that they all follow necessarily as conse- 
quences of the law of gravitation, which he had discovered ; 
namely, that " every particle of matter in the universe 
attracts every other particle with a force that varies directly 
as the masses of the particles, and inversely as the square of 
the distance between them." It would take us far beyond 
our limits to attempt to show how Kepler's laws follow 
from this, but they do. The only mystery in the case is 
the mystery of the "attraction" itself; for this word 
"attraction" is to be taken as simply describing an effect 
without in the least explaining it. 

Things take place as if the atoms had in themselves intelligence 
to recognize each other's positions, and power to join hands in some 
way, and pull upon each other through the intervening space, whether 
it be great or small. But neither Newton nor any one else supposes 
that atoms are really endowed with any such power, and the expla- 
nation of gravity remains to be found. Very probably it is somehow 
involved in that constitution of the material universe which makes 
possible the transmission of light and heat and electric and mag- 
netic forces through space apparently empty, but probably filled with 
that mysterious substance " the ether " of the physicists. 

222. Sufficiency of Gravitation to explain the Planetary- 
Motions. — We wish to impress as distinctly as possible 
upon the student one idea, this namely, that given a 



192 



LESSONS IX ASTRONOMY 



planet once in motion, nothing further than gravitation is 
required to explain perfectly all its motions forever after. 
Many half-educated people have an idea, that some other 
force or mechanism must act to keep the planets going. 




Fig, 49. — The Smaller Planetary Orbits 

This is not so: not a single motion in the whole planetary 

system lias ever yet been detected lor which gravitation 

fails to account. 

223. Map of the Orbits. — Fig. 49 shows the smaller 
orbits of the system (including the orbit of Jupiter), drawn 



THE PLANETS IX GENERAL 



193 



to scale, the radius of the earth's orbit being taken as 
four-tenths of an inch. * 

On this scale, the diameter of Saturn's orbit would be 7.4 inches, 
that of Uranus would be 13.4 inches, and that of Neptune about 
2 feet. The nearest fixed star, on the same scale, would be a mile 
and a quarter away. 

It will be seen that the orbits of Mercury, Mars, Jupiter, 
and several of the asteroids are quite distinctly " out of 
center " with respect to the sun. The orbits are so nearly 
circular that there is no noticeable difference between their 
length and their breadth, but the eccentricity shows plainly 
in the position of the sun. 

224. Inclination of the Orbits. — The orbits are drawn 
as if they all lay on the plane of the ecliptic, i.e., on the 
surface of the paper. 
This is not quite cor- 
rect. The orbit of the 
asteroid Pallas should 
be really tipped up at 
an angle of nearly 30°, 
and that of Mercury, 
which is more inclined 

to the ecliptic than the orbit of any other of the principal 
planets, is sloped at an angle of 7°. The inclinations, how- 
ever, are so small (excepting the asteroids) that they may be 
neglected for ordinary purposes. On the scale of the dia- 
gram, Neptune, which rises and falls the most of all with ref- 
erence to the plane of the ecliptic, would never be more than 
a third of an inch above or below the level of the paper. 

The line in which the plane of a planet's orbit cuts the 
plane of the earth's orbit at the ecliptic is called the Line 




Fig. 50. — Inclination and Line of Nodes 



194 



LESSONS IN ASTRONOMY 



of Nodes. Fig. 50 shows how the line of nodes and, i, 
the inclination of the two orbits, are related. 

225. Geocentric Motions of the Planets, i.e., their Motions 
with Respect to the Earth regarded as the Center of Obser- 
vation. — While the planets revolve regularly in nearly cir- 
cular orbits around the sun, with velocities 1 which depend 
upon their distance from it, the motions relative to the earth 
are very different, being made up of the planet's real motion 

combined with the appar- 
ent motion due to that 
of the earth in her own 
orbit. 

If, for instance, we 
keep up observations, for 
a long time, of the direc- 
tion of Jupiter as seen 
from the earth, at the 
same time watching the 
changes of its distance 
by measuring the alter- 
ations of the planet's 
apparent size as seen in 
the telescope, and then plot the results to get the form of 
the orbit of Jupiter with reference to the earth, we get a 
path like that shown in Fig. 51, which represents his 
motion relative to the earth during a term of about 
twelve years. The appearances are all the same as if the 
earth were really at rest while the planet moved in this 
odd way. 

18.5 
1 A planet's velocity in miles per second equals very nearly 




Fig. 51.- 



- Apparent Geocentric Motion of 
Jupiter 



the distance being expressed as in Sec. 218. 



VDistance 



THE PLANETS IN GENERAL 



195 



The procedure for finding this relative, or geocentric, orbit of 
Jupiter is the same as that indicated in Appendix, Sec. 428, for find- 
ing the form of the earth's orbit around the sun. 

226. Direct and Retrograde Motion. — With the eye alone 
the changes in a planet's diameter would not be visible, 
and we should notice only the alternating direct (eastward) 
and retrograde (westward) motion of the planet among the 
stars. If we watch one of the planets (say Mars) for a 
few weeks, beginning at the time when it rises at sunset, 




Fig. 52. — Apparent Motions of Saturn and Uranus in 1897 

we shall find that each night it has traveled some little 
distance to the west; and it will keep up this westward 
or retrograde motion for some weeks, when it will stop or 
become "stationary," and will then reverse its motion 
and begin to move eastward. If we watch long enough 
(i.e., for several years), we shall find that it keeps up this 
oscillating motion all the time, the length of its eastward 
swing being always greater than that of the corresponding 
westward one. Fig. 52 shows the alternate progression 
and retrogression of Saturn and Uranus during 1897. All 



196 



LESSONS IN ASTRONOMY 



the planets, without exception, behave alike in this respect, 
as to their alternate direct and retrograde motion among 
the stars. 

227. Elongation and Conjunction. — The visibility of a 
planet does not, however, depend upon its position among 
the stars, but upon its position in the sky with reference 



Conjunction 




Greatest E. Elongation 



Greatest W. Elongation 



Opposition 
Fig. 53. — Planetary Configurations 

to the sun's place. If it is very near the sun, it will be 
above the horizon only by day, and generally we cannot 
see it. The Elongation of a planet is the apparent distance 
from the sun in degrees, as seen from the earth, of course. 
In Fig. 53, for the planet P, it is the angle PES. When 
the planet is in line with the sun as seen from the earth, 
at B, C, or I in the figure, the elongation is zero, and the 



THE PLANETS IN GENERAL 197 

planet is said to be in conjunction ; inferior conjunction, 
if the planet is between the earth and the sun, as at I; 
superior, if beyond the sun, as at B or C. When the 
elongation is 180°, as at A, the planet is said to be in 
opposition. When the planet is at an elongation of 90°, 
as at F or G, it is in quadrature. Evidently only those 
planets which lie within the earth's orbit, and are called 
" inferior " planets, can have an inferior conjunction ; and 
only those which are outside the earth's orbit (the " supe- 
rior" planets) can come to quadrature or opposition. 

228. Synodic Period. — The synodic period of a planet is 
the time occupied by it in passing from conjunction to con- 
junction again, or from opposition to opposition ; so called 
because the word " synod " is derived from two Greek 
words which mean " a coming together." The relation 
of the synodic period to the sidereal is the same for planets 
as in the case of the moon. If E is the length of the 
true (sidereal) year, and P the planet's sidereal period, S 
being the length of the synodic period, then 

1_1_1 
S~E P 

(The difference between — and — is to be taken without 

E P 

regard to which of the two is the larger.) 

229. The Synodic Motion, or Apparent Motion of a Planet 
with Respect to " Elongation' ' or to the Sun's Place in the 
Sky. — In this respect there is a marked difference between 
the superior and inferior planets. 

(a) The inferior planets are never seen very far from 
the sun, but appear to oscillate back and forth in front of 
and behind him. Venus, for instance, starting at superior 



198 LESSONS IN ASTRONOMY 

conjunction at C (Fig. 53), seems to come out eastward 
from the sun as an evening star, until, at the point T 7 , she 
reaches her greatest eastern elongation, about 47° from the 
sun. Then she begins to diminish her elongation, and 
approaches the sun, until she comes to inferior conjunc- 
tion, at 7. From there she continues to move westward as 
morning star, until she comes to V ! , her greatest western 
elongation, and there she begins to diminish her western 
elongation until, at the end of the synodic period, she is 
back at superior conjunction. The time taken to move 
from V' to V through C is, in her case, more than three 
times that required to slide back from V to V through L 
The gain of eastern elongation is uphill work, as she is 
then, so to speak, pursuing the sun, which itself moves east- 
ward nearly a whole degree every day along the ecliptic. 

(b) The superior planets may be found at all elonga- 
tions, and do not oscillate back and forth with reference 
to the apparent place of the sun, but continually increase 
their western elongation or decrease their eastern. They 
always come to the meridian earlier on each successive night, 
though the difference is not uniform. 

230. Ptolemaic and Copernican Systems. — Until the 
time of Copernicus (about 1540) the Ptolemaic system 
prevailed unchallenged. It rejected the idea of the earth's 
rotation (though Ptolemy accepted the rotundity of the 
earth), placing her at the center of things and teaching 
that the apparent motions of the stars and planets were 
real ones. It taught that the celestial sphere revolves daily 
around the earth, carrying the stars and planets with it, 
and that besides this diurnal motion, the moon, the sun, 
and all the planets revolve around the earth within the 



THE PLANETS IN GENERAL 199 

sphere, the two former steadily, but the planets with the 
peculiar looped motion shown in Fig. 51. 

Copernicus put the sun at the center, making the earth 
revolve on its axis and travel around the sun, and showed 
that it was possible in this simple way to account for all 
the otherwise hopelessly complicated phenomena of the 
planetary and diurnal motions, so far as then known. It 
was not until after the invention of the telescope and the 
introduction of new methods of observation that the facts 
which absolutely demonstrated the orbital motion of the 
earth were brought to light, viz., Aberration of Light 
(Appendix, Sec. 435) and Stellar Parallax (Sec. 433). 

THE PLANETS THEMSELVES 

231. In studying the planetary system we meet a num- 
ber of inquiries which refer to the planet itself and not to 
its orbit, relating, for instance, to its magnitude ; its mass, 
density, and surface gravity ; its diurnal rotation and oblate- 
ness; its brightness, phases, and reflecting power, or " albedo"; 
the peculiarities of its spectrum ; its atmosphere ; its surface 
markings and topography ; and, finally, its satellite system. 

232. Magnitude. — The size of a planet is found by 
measuring its apparent diameter (in seconds of arc) with 
some form of " micrometer." (See Appendix, Sec. 415.) 
Since we can find the distance of a planet from the earth 
at any moment when we know its orbit, this micrometric 
measure will give us the means of finding at once the 
planet's diameter in miles. 

If we take r to represent the number of times by which 
the planet's semi-diameter exceeds that of the earth, then 



200 LESSON'S IN ASTRONOMY 

the area of the planet's surface compared with that of the 
earth equals r 2 , and its volume or bulk equals r\ The 
nearer the planet, other things being equal, the more 
accurately r and the quantities to be derived from it can 
be determined. An error of O'M in measuring the appar- 
ent diameter of Venus when nearest ns counts Eor less 

than thirteen miles, while in Neptune's ease, the same 
error would correspond to more than 1300 miles. 

233. Mass, Density, and Gravity. If the planet has a 
satellite, its mass is very easily and accurately found from 

the following proportion, which we simply stale without 

demonst ration (see ( reneral Astronomy, Arts. 536, 539), viz, : 

1 8 a 8 
Ma%% of Sun : Mass of Planet : : ■ : — ; 

in which A is the mean distance of the planet from the 
snn and T its sidereal period of revolution, while fl is 
the distance of the satellite from the planet and / its 
sidereal period ; whence 

Mass o\' Planet Snn X ( \, x , 

The calculations indicated are very easy with the help of loga- 
rithms, and if the student lias learned to use them it will he well for 
him bo verify some of the planet, masses from the data for the satel- 
lites given in Table 1 1 1, p. 408. 

Substantially the same proportion may he wsrd to compare the 
planet wit h t he earl h, viz, ! 

(Earth t Moon) ; (Planet I Satellite) :: "'., : ""., ; 

V *% 

d { and /, being here the period and distance of the moon, and </., 
and /., those of the planet's satellite. 

If the planet has no satellite, the determination of its 
mass is a, difficult matter, depending upon perturbations 
produced by it in the motions of the other planets. 



THE PLANETS IX GENERAL 201 

Having the planet's mass compared with the earth, we 
get its density by dividing the mass by the volume, and 
the superficial gravity is found by dividing by r 2 the mass 
of the planet compared with that of the earth. 

234. The Rotation Period and Data connected with it. - 
The length of the planet's day, when it can be determined 
at all, is ascertained by observing with the telescope some 
spot on the planet's disk, and noting the interval between 
its returns to the same apparent position. The inclination 
of the planet's equator to the plane of its orbit, and the 
position of its equinoxes, are deduced from the same 
observations that give the planet's diurnal rotation ; we 
have to observe the path pursued by a spot in its motion 
across the disk. Only Mars, Jupiter, and Saturn permit 
us to find these elements with any considerable accuracy. 

The ellipticity or oblateness of the planet, due to its 
rotation, is found by taking measures of its polar and 
equatorial diameters. 

235. Data relating to the Planet's Light. — A planet's 
brightness and its reflecting power, or " albedo," are deter- 
mined by photometric observations, and the spectrum of the 
planet's light is of course studied with the spectroscope. 
The question of the planet's atmosphere is investigated by 
means of various effects upon the planet's appearance and 
light, and by the phenomena that occur when the planet 
comes very near to a star or to some other heavenly body 
which lies beyond. The planet's surface markings and 
topography are studied directly with the telescope, by mak- 
ing careful drawings of the appearances noted at different 
times. Photography, also, is beginning to be used for 
the purpose. If the planet has any well-marked and 



202 LESSONS IN ASTRONOMY 

characteristic spots upon its surface by which the time of 
rotation can be found, then it soon becomes easy to identify 
such as are really permanent, and after a time we can 
chart them more or less perfectly ; but we add at once that 
Mars is the only planet of which, so far, we have been able 
to make anything which can be fairly called a map. 

236. Satellite System. — The principal data to be ascer- 
tained are the distances and periods of the satellites. These 
are obtained by micrometric measures of the apparent 
distance and direction of each satellite from the planet, fol- 
lowed up for a considerable time. In a few cases it is pos- 
sible to make observations bv which Ave can determine the 
diameters of the satellites, and when there are a number 
of satellites together their masses may sometimes be ascer- 
tained from their mutual perturbations. With the excep- 
tion of our moon and Iapetus, the outer satellite of Saturn, 
all the satellites of the solar system move almost exactly 
in the plane of the equator of the planet to which they 
belong, — at least so far as known, for we do not know 
with certainty the position of the equators of Uranus and 
Neptune. Moreover, all the satellites, except the moon 
and Hyperion, the seventh satellite of Saturn, move in 
orbits that are very nearly circular. 

237. Tables of Planetary Data. — In the Appendix we 
present tables of the different numerical data of the solar 
system, derived from the best authorities and calculated 
for a solar parallax of 8".80, the sun's mean distance being 
therefore taken as 92,897000 miles. These tabulated 
numbers, however, differ widely in accuracy. The periods 
of the planets and their distances in " astronomical units " 
are very accurately known ; probably the last decimal in 
the table may be trusted. Next in certainty come the 



THE PLANETS IN GENERAL 



203 



masses of such planets as have satellites, expressed in terms 
of the sun's mass. The masses of Venus and Mercury are 
much more uncertain. 

The distances of the planets in miles, their masses in 
terms of the earth's mass, and their diameters in miles, all 
involve the solar parallax and are affected by the slight 
uncertainty in its amount. For the remoter planets, 




Fig. 54. — Relative Size of the Planets 



diameters, volumes, and densities are all subject to a very 
considerable percentage of error. The student need not 
be surprised, therefore, at finding serious discrepancies 
between the values given in these tables and those given 
in others, amounting in some cases to ten or twenty per 
cent, or even more. Such differences merely indicate the 
actual uncertainty of our knowledge. Fig. 54 gives an 
idea of the relative sizes of the planets. 



204 LESSONS IN ASTRONOMY 

The sun, on the scale of the figure, would be about a 
foot in diameter. 

238. Sir John HerschePs Illustration of the Dimensions of the 
Solar System. — In his "Outlines of Astronomy," Ilerschel gives 
the following illustration of the relative magnitudes and distances 
of the members of our system : 

Choose any well-levelled field. On it place a globe two feet in 
diameter. This will represent the sun. Mercury will be represented by 
a grain of mustard seed on the circumference of a circle 164 feet in 
diameter for its orbit ; Venus, a pea, on a circle of 284 feet in diameter ; 
the Earth, also a pea, on a circle of 430 feet ; Mars, a rather large pin's 
head, on a circle of 654 feet ; the asteroids, grains of sand, on orbits hav- 
ing a diameter of 1000 to 1200 feet ; Jupiter, a moderate-sized orange, on 
a circle nearly half a mile across ; Saturn, a small orange, on a circle of 
four-fifths of a mile ; Uranus, a full-sized cherry or small plum, upon a 
circumference of a circle more than a mile in diameter ; and, finally, 
Neptune, a good-sized plum, on a circle about 2-J- miles in diameter. 

We may add that on this scale the nearest star w r ould be on the 
opposite side of the earth, 8000 miles away. 



THE TERRESTRIAL PLANETS — MERCURY, VENUS, 
AND MARS 

MERCURY 

239. Mercury has been known from the remotest antiq- 
uity, and among the Greeks it had for a time two names, 
— Apollo when it was morning star, and Mercury when it 
was evening star. It is so near the sun that it is com- 
paratively seldom seen with the naked eye, but when near 
its greatest elongation it is easily enough visible as a bril- 
liant reddish star of the first magnitude, low down in the 
twilight. It is best seen in the evening at such eastern 



MERCURY 205 

elongations as occur in the spring. When it is morning 
star it is best seen in the autumn. 

It is exceptional in the solar system in various ways. It is 
the nearest planet to the sun. receives the most light and heat* 
is the swiftest in its movement, and (excepting some of the 
asteroids) has the most eccentric orbit, with the greatest inclina- 
tion to the ecliptic. It is also the smallest in diameter (again 
excepting the asteroids), has the least mass, and (perhaps) 
the greatest density of all the planets, but the latest results 
place it below both Venus and the earth in this respect. 

240. Its Orbit. — The planet's mean distance from the 
sun is 36.000000 miles, but the eccentricity of its orbit is 
so great (0.205) that the sun is 7,500000 miles out of the 
center, and the distance ranges all the way from 28^ 
to 43^ millions, while the planet's velocity in the differ- 
ent parts of its orbit varies from 36 miles a second to 
only 23. A given area upon its surface receives on the 
average nearly seven times as much light and heat as it 
would on the earth ; but the heat received when the planet 
is at perihelion is 2i times greater than at aphelion. For 
this reason there must be at least two seasons in its year, 
due to the changing distance of the planet from the sun. 
whatever may be the position of its equator or the length 
of its day. The sidereal period is 88 days, and the syn- 
odic period (or time from conjunction to conjunction) is 
116 days. The greatest elongation ranges from 18° to 28°, 
and occurs about 22 days before and after the inferior 
conjunction. The inclination of the orbit to the ecliptic 
is about 7°. 

241. Planet's Magnitude, Mass, etc. — The apparent 
diameter of Mercury varies from 5" to about 13", according 



206 LESSONS IN ASTRONOMY 

to its distance from us, and its real diameter is very 
near 3000 miles. This makes its surface about ^ that of 
the earth, and its bulk, or volume, ^ . The planet's mass 
is very difficult to determine, since it has no satellite, and 
consequently it is not accurately known. Probably it is 
about Jy °f the earth's mass ; it is certainly smaller than 
that of any other planet (asteroids excepted). 

Our uncertainty as to the mass prevents us from assign- 
ing certain values to its density or superficial gravity ; but 
if its mass as given above is correct, it is probably about 




Fig. 55. — Phases of Mercury and Venus 

two-thirds as dense as the earth, and the force of gravity 
upon it is about one-quarter what it is upon the earth. 

242. Telescopic Appearances, Phases, etc. — Seen* through 
the telescope the planet looks like a little moon, showing 
phases precisely similar to those of our satellite. At infe- 
rior conjunction the dark side is towards us, at superior con- 
junction the illuminated surface. At greatest elongation 
the planet appears as a half-moon. It is gibbous between 
superior conjunction and greatest elongation, while between 
inferior conjunction and greatest elongation it is crescent. 
Fig. 55 illustrates these phases. 



MERCURY 207 

The atmosphere of the planet cannot be as dense as that 
of the earth or Venus, because at a transit it shows no 
encircling ring of light, as Venus does (Sec. 248). Both 
Huggins and Vogel, however, report that the spectrum of 
the planet, in addition to the ordinary dark lines belonging 
to the spectrum of reflected sunlight, shows certain bands 
known to be due to water-vapor, thus indicating that water 
exists in the planet's atmosphere. 

Generally Mercury is so near the sun that it can be 
observed only by day, but when proper precautions are 
taken to screen the object-glass of the telescope from direct 
sunlight, the observation is not especially difficult. The 
surface presents very little of interest. The disk is brighter 
at the edge than at the center, but the markings are not 
well enough defined to give us any really satisfactory 
information as to its topography. 

The albedo, or reflecting power, of the planet is very 
low, — only 0.13, somew^hat inferior to that of the moon 
and very much below that of any other of the planets. 
Xo satellite is known, and there is no reason to suppose 
that it has any. 

243. Diurnal Rotation of the Planet. — In 1889 Schia- 
parelli, the Italian astronomer, announced that he had dis- 
covered certain markings upon the planet, and that they 
showed that the planet rotates on its axis only once daring 
its orbital period of eighty-eight days, thus keeping the 
same face always turned towards the sun, in the same way 
that the moon behaves with respect to the earth. Owing 
to the eccentricity of the planet's orbit, however, it must 
have a large libration (Sec. 145), amounting to about 23i° 
on each side of the mean : i.e., seen from a favorable station 



208 LESSONS IN ASTRONOMY 

on the planet's surface, the sun, instead of rising and set- 
ting as with us, would seem to oscillate back and forth 
through an arc of 47° once in 88 days. 

This asserted discovery is very important and has excited 
great interest. Schiaparelli is probably correct, and Lowell 
at the Flagstaff Observatory corroborates him; but some 
are still skeptical, and it may be well to wait for confir- 
mation of his observations by others before absolutely 
accepting the conclusion. 

244. Transits of Mercury. — At the time of inferior 
conjunction the planet usually passes north or south of 
the sun, the inclination of its orbit being 7°; but if the 
conjunction occurs when the planet is very near its node 
(Sec. 224), it crosses the sun's disk and becomes visible 
upon it as a small black spot, — not, however, large enough 
to be seen without a telescope, as Venus can under similar 
circumstances. Since the earth passes the planet's line of 
nodes on May 7 and November 9, transits can occur only 
near those days, and certain peculiarities in the planet's 
orbit make the November transits about twice as numerous 
as those that come in May. 

The last of these transits occurred on May 9, 1891, and Nov. 10, 
1891; the next will occur in November, 1907 and 1914, and in 
May, 1924. 

Only the two first of these will be visible in the United States, 
and not the entire transit in either case. 

Transits of Mercury are of no particular astronomical importance, 
except as furnishing accurate determinations of the planet's place in 
the sky at a given time. 



VENUS 209 



VENUS 



245. The second planet in order from the sun is Venus, 
the brightest and most conspicuous of all. It is so brilliant 
that at times it casts a shadow, and is often easily seen by 
the naked eye in the daytime. Like Mercury, it had two 
names among the Greeks, — Phosphorus as morning star, 
and Hesperus as evening star. 

Its mean distance from the sun is 67,200000 miles, and 
its distance from the earth ranges from 26,000000 miles 
(93-67) tol60,000000 (93 + 67). No other body ever comes 
so near the earth except the moon, and occasionally a comet. 
The eccentricity of the orbit of Venus is the smallest in the 
planetary system, only 0.007, so that the greatest and least 
distances of the planet from the sun differ from the mean less 
than 500,000 miles. Its sidereal period is 225 days, or 
seven months and a half, and its synodic period 584 days, 
— a year and seven months. From inferior conjunction 
to greatest elongation is only 71 days. The inclination of 
its orbit is not quite 3i°, — less than half that of Mercury. 

246. Magnitude, Mass, Density, etc. — The apparent 
diameter of the planet varies from 67" at the time of 
inferior conjunction to only 11" at superior, the great dif- 
ference arising from the enormous variation in the distance 
of the planet from the earth. The real diameter of the 
planet in miles is about 7700. Its surface compared with 
that of the earth is -^\ ; its volume, j-^- ^J means °f 
the perturbations she produces upon the earth, the mass of 
Venus is found to be not quite four-fifths of the earth's 
mass, so that her mean density is a little less than the 
earth's. In magnitude she is the earth's twin sister. 



210 LESSONS IN ASTRONOMY 

247. General Telescopic Appearance, Phases, etc. — The 
general telescopic appearance of Venus is striking on 
account of her great brilliancy, but exceedingly unsatisfac- 
tory, because nothing is distinctly outlined upon the disk. 

When about midway between greatest elongation and 
inferior conjunction the planet has an apparent diameter 
of 40", so that, with a magnifying power of only 45, she 
looks exactly like the moon four days old, and of the same 
apparent size. (Very few persons, however, would think 
so on the first view through the telescope ; the novice 
always underrates the apparent size of a telescopic object.) 

The phases of Venus were first discovered by Galileo in 1610, and 
afforded important evidence as to the truth of the Copernican system 
as against the Ptolemaic. 

Fig. 56 represents the planet's disk as seen at five points in its orbit. 
1, 3, and 5 are taken at superior conjunction, greatest elongation, and 
near inferior conjunction, respectively, while 2 and 4 are at intermedi- 
ate points. (No. 2 is badly engraved, however ; the sharp corners are 
impossible since a " terminator " is always a semi-ellipse (Sec. 146)). 

The planet attains its maximum brightness when its 
apparent area is at a maximum, about thirty-six days before 
and after inferior conjunction. According to Zollner, the 
" albedo " of the planet is 0.50; i.e.., it reflects about half the 
light which falls upon it, the reflecting power being about 
three times that of the moon and almost four times that of 
Mercury. It is, however, slightly exceeded by the reflect- 
ing power of Uranus and Jupiter, while that of Saturn is 
about the same. The high albedo is, by most astronomers, 
considered to indicate a surface mostly covered with clouds, 
since few rocks or soils could match its brightness. (But 
see Sec. 249.) Like Mercury, Mars, and the moon, the disk 



VENUS 



211 



of Venus is brightest at the edge, — in contrast with the 
appearance of Jupiter and Saturn. 

248. Atmosphere of the Planet. — There is no question 
that it has an atmosphere of some density. When the 
planet is half-way upon the sun's disk at the time of a 
" transit," the dark part of the planet outside the sun is 
encircled by a thin line of light due to the refraction, 




Fig. 5(J. — Telescopic Appearances of Venus 



reflection, and scattering of sunlight by the planet's atmos- 
phere. And when the planet is near the sun, at the time 
of inferior conjunction, the horns of its crescent extend far 
beyond the diameter. When very near, as in 1898, the 
horns coalesce, and the brightest part of the complete ring 
is then on the side next the sun, showing that the illumina- 
tion is then due mainly to reflection and not to refraction 



212 



LESSONS IN ASTRONOMY 






as formerly supposed. The height and density of its 
atmosphere appear to be about two-thirds as great as that 
of the earth. Fig. 57 represents the appearance noted by 
Vogel during the transit of 1882. 

The presence of water-vapor was announced by some of 
the earlier spectroscopists, but later observations fail to 

confirm it, leaving 
the fact somewhat 
doubtful. Many 
observers have also 
reported faint lights 
as visible at times 
on the dark por- 
tions of the planet's 
disk. These cannot 
be accounted for by 
any mere reflection 
or refraction of sun- 
light, but must orig- 
inate on the planet 
itself. They recall 
the Aurora Borealis 
and other electrical 
manifestations on 
the earth, though it is impossible to give a certain expla- 
nation of them as yet. 

249. Surface Markings, Rotation, etc. — As has been said, 
Venus is a very unsatisfactory telescopic object. She pre- 
sents no obvious surface markings, — nothing but occasional 
indefinite shadings. Sometimes, however, when in the cres- 
cent phase, intensely bright spots have been reported near 





Fki. 57.- 



- Atmosphere of Venus as seen during 
a Transit 
Vogel, 1882 



VENUS 213 

the points of the crescent, which may perhaps be " ice-caps'' 
like those which are seen on Mars. The darkish shadings 
may possibly be continents and oceans, dimly visible, but 
the prevailing impression is that they are cloudlike and 
purely atmospheric, the real surface of the planet being 
always hidden. 

Fig. 58 is from drawings made by Mascari at the observa- 
tory on Mt. Etna, and is an excellent representation of the 
appearance of the planet in a good telescope. 




Fig. 58. — Venus 
After Mascari 

As to the rotation period of the planet, nothing is yet 
certainly known. The length of its day has been set, on 
very insufficient grounds, at about 23 h 21 m ; but the recent 
work of Schiaparelli makes it almost certain that this result 
cannot be trusted, and renders it rather probable that Venus 
behaves like Mercury in its diurnal rotation, the length of 
its sidereal day being equal to the time of its orbital revo- 
lution. Lowell indeed asserts this positively, but certain 
other observers still maintain the correctness of the old 
period. The spectroscope may possibly settle the question 
on Doppler's principle (Sec. 179), by showing how rapidly 



214 LESSONS IN ASTRONOMY 

the, rdgu of the planet's disk moves towards or from the 
earth. Some preliminary attempts have however failed to 
yield any satisfactory result. 

The planet's disk shows no sensible oblateness. 
No satellite has ever been discovered; not, however, for 
want of earnest searching. 

250. Transits. — Occasionally Venus passes between the 
earth and the sun at inferior conjunction, oivino- us a 
so-called " transit." She is then visible, even to the naked 
eye, as a black spot on the sun's disk, crossing it from east 
to west. When the transit is central it occupies about 
eight hours, but when the track lies near 
^f" the edge of the disk the duration is cor- 

respondingly shortened. Since the earth 
passes the nodes of the orbit on June 5 
and December 7, all the transits occur 
near these days, but they are extremely 
rare phenomena. Their special interest 

Fig. 59. — Transit of consists in their availability for the pur- 
Venus Tracks c t - ^^ ii j * n /o 

pose or nnaing the sun s parallax. (See 
Appendix, Sec. 487, and General Astronomy, Chap. XVI.) 

The first observed transit in 1639 was seen by only two persons, — 
llorrox and Crabtree, in England, — but the fourwhich have occurred 

since (hen have been observed in all parts of the world by scientific 

expeditions sent out for the purpose by the different governments. 

The transits of 170!) and L882 were visible in the United States. 

Transits of Yenns have occurred or will occur at the following dates : 

Dec. 7, L681, Dec. 1, K)")!), Dec. 0, 1874, Dec. (>, 1882, 
June :>, L761, dune 8, 17(H), dune 8, 2004, June <>, 2012. 

Fig. 58 shows the (racks of Venus across the sun's disk during the 
transits of 1*7 1 and L882, 




MARS 215 



MARS 



251. This planet, also, has always been known. It is so 
conspicuous on account of its fiery red color and brightness, 
as well as the rapidity and apparent capriciousness of its 
movement among the stars, that it could not have escaped 
the notice of the very earliest observers. 

Its mean distance from the sun is a little more than one 
and a half times that of the earth (141,500000 miles), and 
the eccentricity of its orbit is so considerable (0.093) that 
its radius vector varies more than 26,000000 miles. At 
opposition the planet's average distance from the earth is 
48,600000 miles; but when opposition occurs near the 
planet's perihelion this distance is reduced to less than 
36,000000 miles, while near aphelion it is over 61,000000. 
At conjunction the average distance from the earth 
is 234,000000. 

The apparent diameter and brightness of the planet, of 
course, vary enormously with these great changes of dis- 
tance. At a favorable opposition (when the planet's 
distance from us is the least possible) it is more than fifty 
times as bright as at conjunction and fairly rivals Jupiter ; 
when most remote, it is hardly as bright as the Pole-star. 

The favorable oppositions occur always in the latter part of 
August and at intervals of fifteen or seventeen years. The last such 
opposition was in 1892, and the next will be in 1907. 

The inclination of the orbit is small, — 1° 51'. The 
planet's sidereal period is 687 days (one year, ten and a 
half months) ; its synodic period is much the longest in 
the planetary system, being 780 days, or nearly two years 



216 



LESSONS m ASTRONOMY 



and two months. During 710 of these 780 days it moves 
towards the east, and retrogrades during 70. 

252. Magnitude, Mass, etc. — The apparent diameter of 
the planet ranges from 3".6 at conjunction to 25" at a 
favorable opposition. Its real diameter is approximately 
4300 miles, with an error of perhaps 50 miles one way or 
the other. This makes its surface about two-sevenths, and 
its volume one-seventh of the earth's. Its mass is a little 

less than one-ninth of the 
earth's mass, its density 
0.73, and its superficial grav- 
ity 0.38 ; i.e., a body which 
here weighs 100 pounds 
would have a weight of only 
38 pounds on the surface 
of Mars. 

253. General Telescopic 
Aspect, Phases, etc. — When 
the planet is nearest it is 
more favorably situated for 
telescopic observation than 
any other heavenly body, 
the moon alone excepted. 
It then shows a ruddy disk which, with a magnifying 
power of 75, is as large as the moon. Since its orbit 
is outside the earth's, it never exhibits the crescent 
phases like Mercury and Venus ; but at quadrature it 
appears distinctly gibbous, as in Fig. 60, about like the 
moon three days from full. Like Mercury, Venus, and the 
moon, its disk is brightest at the limb (i.e., at its circular 
edge) ; but at the " terminator," or boundary between day 




Fig. 60. — Mars near Quadrature 
Lowell, 1894 



MARS 217 

and night upon the planet's surface, there is a slight 
shading which, taken in connection with certain other 
phenomena, indicates the presence of an atmosphere. 
This atmosphere, however, is probably much less dense 
than that at the earth, as indicated by the infrequency of 
clouds and of other atmospheric phenomena familiar to us 
on the earth. Huggins and Vogel have reported that the 
planet's spectrum shows the lines of water-vapor ; but the 
later observations of Campbell, at the Lick Observatory, 
do not confirm this and go to show that whatever atmos- 
phere exists must be very rare indeed, not more than 
one-fourth as dense as our own, and probably less. 

Zollner gives the albedo of Mars as 0.26, — just double 
that of Mercury, and much higher than that of the moon, 
but only about half that of Venus and the major planets. 
Near opposition the brightness of the planet suddenly 
increases in the same way as that of the moon near the 
full (Sec. 149). 

254. Rotation, etc. — The spots upon the planet's disk 
enable us to determine its period of rotation with great 
precision. Its sidereal day is found to be 24 h 37 m 22 s .6T, 
with a probable error not to exceed one-fiftieth of a second. 
It is the only one of the planets which has the length of its 
day determined with any such accuracy. The exactness is 
obtained by comparing the drawings of the planet made 
two hundred years ago with others made recently. . 

The inclination of the planet's equator to the plane of 
its orbit is very nearly 24° 50' (26° 21' to the ecliptic). So 
far, therefore, as depends upon that circumstance, Mars 
should have seasons substantially the same as our own, and 
certain phenomena make it evident that such is the case. 



218 LESSONS IN ASTRONOMY 

The planet's rotation causes a slight flattening of the 
poles, — hardly sensible to observation, but probably about 
Tj-i-Q. (Larger values, now known to be erroneous, are given 
in many text-books.) 

255. Surface and Topography. — With even a small tele- 
scope, not more than four or five inches in diameter, the 
planet is a very beautiful object, showing a surface diver- 
sified with markings light and dark, which, for the most 
part, are found to be permanent. Occasionally, however, 
we see others of a temporal character, supposed to be 
clouds ; but these are surprisingly rare as compared with 
clouds upon the earth. The permanent markings are 
broadly divisible into three classes. 

First, the white patches, two of which are specially con- 
spicuous near the planet's poles and are generally supposed 
to be masses of snow or ice, since they behave just as would 
be expected if such were the case. The northern one 
dwindles away during the northern summer, when the north 
pole is turned towards the sun, while the southern one grows 
rapidly larger ; and vice versa during the southern summer. 

Second, patches of bluish gray or greenish shade, covering 
about three-eighths of the planet's surface and generally 
supposed to be bodies of water, though this is very far 
from certain. 

Third, extensive regions of various shades of orange and 
yellow, covering nearly five-eighths of the surface, and 
interpreted as land. 

These markings are, of course, best seen when near 
the center of the planet's disk ; near the limb they are 
lost in the brilliant light which there prevails, and at the 
terminator they fade out in the shade. 



MARS 



219 



Fig. 61, from drawings by the late ]\ rax well Green of Madeira, 
gives an excellent idea of the usual appearance of the planet under 
favorable conditions. 

256. Recent Discoveries ; the Canals and their Gemi- 
nation. — In addition to these three classes of markings 
the Italian astronomer Schiaparelli, in 1877 and 1879, 
announced the discovery of a great number of fine straight 
lines, or " canals," as he called them, 
crossing the ruddy portions of the 
planet's surface hi various directions, 
and in 1881 he announced that many 
of them become double at times. For 
several years some doubt remained, 
because other observers, with tele- 
scopes more powerful than his, were 
unable to make out anything of the 
sort. More recently, however, his 
results have been abundantly con- 
firmed both in Europe and in this 
country. It appears that the power 
of the telescope is not so important 
in the observation of these objects as 
steadiness of the air and keenness 
of the observer's eye. Nor are they 
usually best seen when Mars is nearest, but their visi- 
bility depends upon the season on the planet ; and this 
is especially the case with their " gemination." There 
is, however, considerable reason to suspect that this 
peculiar doubling is merely an illusion, due to imperfect 
focusing of the telescope or a slight astigmatism of the 
observer's eye. 




Fig. 61. — Telescopic 

Views of Mars 

Green, 1878 



220 LESSONS IJST ASTRONOMY 

As to the real nature of these markings and their behav- 
ior there is wide difference of opinion, and it is doubtful if 
the true explanation has yet been proposed. According to 
Mr. Lowell, the polar caps are really snow masses, which 
melt in the (Martian) spring, and the water makes its 
way towards the equator over the planet's mountainless 
plains, obscuring for several weeks the well-known mark- 
ings which are visible at other times. For him the dark por- 
tions of the planet's surface are not seas, but land covered 
with vegetation of some sort, while the ruddy portions are 
rocky deserts, intersected by the " canals," which, in his 
view, are really irrigating water courses ; and on account of 
their straightness he is disposed to accept them as artificial. 
When the waters reach these canals vegetation springs up 
along their banks on either side, and these streaks of vegeta- 
tion are what we see. Where the water courses cross each 
other there are dark round " lakes," as they have been 
called, which he interprets as oases. 

Of course the difficulties of the theory are obvious : for 
instance, the almost absolute levelness of the planet's sur- 
face which it assumes, and especially the fact that at Mars 
the solar radiation is only half as intense as upon the earth. 
This, recalling the low density of his atmosphere, would 
naturally lead to the supposition that the temperature 
even at his equator must be lower than that at the sum- 
mits of our highest mountains, and far below the freez- 
ing point of water. It was this consideration that has led 
some astronomers to suggest that the polar caps are not ice- 
sheets at all, but formed of congealed carbon dioxide (C0 2 ), 
or some substance which remains liquid and vaporous at 
much lower temperatures than water. 



MARS 221 

But whatever the explanation may be, there is no longer 
much doubt that the " canals " are real, and that the surface 
of the planet undergoes noticeable changes of appearance 
with the progress of the planet's seasons, as shown by 
Fig. 62, from drawings made by Barnard at the Lick 
Observatory in 1894. At the same time Professor Holden 
of the Lick Observatory says that during the years 1888- 
1895 nothing has been observed there, so far as he knows, 
which goes to confirm Mr. Lowell's " very positive and 
striking conclusions." 

The day may perhaps come when photography will be 
able to lend its aid to the solution of the problem, or some 




Fig. 62. — Seasonal Changes on Mars 
Barnard 

heat measurer may be contrived sensitive enough to give 
us positive information as to the planet's temperature. If 
the polar caps are really caps of frozen water, Mars must 
obtain surface heat from some still unexplained supply. 

257. Maps of the Planet. — A number of maps of Mars have 
been constructed by different observers since the first one was made 
by Maedler in 1830. Fig. 63 is reduced from one which was pub- 
lished in 1888 by Schiaparelli and shows most of his "canals" and 
their " geminations. " While there may be some doubt as to the 
accuracy of the minor details, there can be no doubt that the main 
features of the planet's surface are substantially correct. The nomen- 
clature, however, is in a very unsettled state. Schiaparelli has taken 



222 LESSONS IN ASTRONOMY 

his names mostly from anoienl geography, while bhe English areog 
raphers, 1 Eollowing bhe analogj of the lunar maps, have mainly used 
bhe names of as1 ronomers who have oontributed bo our knowledge 

o!' I he planet's surface. 

258. Satellites. The planet has two satellites, discov- 
ered by Professor Hall, at Washington, in 1 s 7 7 . They 

are extremely small and obseryable only with yery large 
telescopes. The outer one, Deimos, is at a, distance of 
14,600 miles from the planet's center and has a sidereal 
period o( 80 to 18 m J while the inner one, PhoboS, is at a dis- 
tance of only 5800 miles and its period is only 7 fe 89 m , 
less than one-third of the planet's day. (This is the only 
cast* of a satellite with a period shorter than the day of its 

primary.) Owing to tins oiroumstanoe, it rises in the west % 

as seen from the planet's surface, and sets in the east, com- 
pleting its strange baokward diurnal revolution in about 
eleven hours. DeimOS, on the other hand, rises in the 
east, l>nt takes nearly L82 hours in its diurnal circuit, 
which is more than four of its months. Both the orbits 
arc sensibly circular and lie very closely in the plane of 
the planet's equator. 

Micrometric measures of the diameters of such small objects are 
impossible; but, from photometric observations, Professor E. C. Pieh 
ering, assuming that they have bhe same reflecting power as thai of 

Mars itself, estimates the diameter of PhoboS as about 7 miles, and 

that of Deimos as 5 or 8, Lowell, however, from his observations 

Of L894, deduces considerably Larger \ allies, /•/;., 10 miles for Deimos 
and 86 for l'hobos. If this is correct, PhoboS, when in tin' zenith of 

an observer on bhe planet's surface, would be about as large as bhe 
moon, bin not so bright, Deimos would be no brighter than Venus, 

1 The Greek name of Mars is Arcs; hence u Areography n Is the 
description of the surface <^ Mars. 



224 LESSONS IN ASTRONOMY 

259. Habitability of Mars. — As to this question we can only 
say that, while the conditions on Mars are certainly very different 
from those prevailing on the earth, the difference is less than in the 
case of any other heavenly body which we can see with our present 
means of observation ; and if life, such as we know life upon the 
earth, can exist upon any of them, Mars is the place. It is much 
more probable, however, that the conditions as to temperature and 
atmosphere differ from our own quite enough to preclude all terres- 
trial forms of life. 

There is at present no scientific ground for belief one way or the 
other as to the habitability of " other worlds than ours," passionately 
as the doctrine has been affirmed and denied by men of opposite 
opinions. 



CHAPTER IX 

THE PLANETS (Continued) 

The Asteroids — Intramereurian Planets and the Zodiacal Light —The Major 
Planets, Jupiter, Saturn, Uranus, and Neptune 

THE ASTEROIDS OR MIXOR PLAXETS 

260. The asteroids 2 are a multitude of small planets 
circling around the sun in the space between Mars and 
Jupiter. It was early noticed that between Mars and 
Jupiter there is a gap in the series of planetary distances, 
and when Bode's law (Sec. 219) was published in 1772 
the impression became very strong that there must be 
a missing planet in the space, — an impression greatly 
strengthened when Uranus was discovered in 1781, at a 
distance precisely corresponding to that law. 

The first member of the group was found by the Sicilian 
astronomer, Piazzi, on the very first night of the nine- 
teenth century (Jan. 1, 1801). He named it Ceres, after 
the tutelary divinity of Sicily. The next year Pallas w r as 
discovered by Olbers. Juno was found in 1 804 by Harding, 
and in 1807 Olbers, who had broached the theory of an 
exploded planet, discovered the fourth, Vesta, the only 
one which is ever bright enough to be easily seen by the 

1 They were first called asteroids (i.e., " starlike " bodies) by Sir 
William Herschel early in the century, because, though really planets, 
the telescope shows them only as stars, without a sensible disk. 

225 



22C LESSONS IN ASTRONOMY 

naked eye. The search was kept up for s me yc ws I ng 
bur without sue ess, - - rchers did nor look for 

small enough objects. The tilth asteroid (Astraea) was 
Found in 1845 by Heneke. an amateur, who had resumed 
rhe subj studying the fainter stars. In 1S47 three 

more wei scovered, and : since then has added 

fir >m one to thirty-eight. They are usually designated 

their "numbers," bur all the older ones also h 
names: thus, Ceres is 3), Thule is (»s . Eros > w . ere. 
At present more than live hund: known, and since 

1S91 the catalogue has growing with rather incon- 

venient rapidity on account of the substitution of pho- 
togxaphy for the old-fash of planet-hunting. 

A large camera is strapped on the back of a scope 

driven by rk. and a nega ring from 5* to 

10 c square ;: the heavens, is taken with an exposure of 
several hours. The thousands : -tars that appear upon 
the plate all show neat round disks, if the has 

kept his teles si lily pointed; but if rhere is a 

planer anywhere in rhe field ir will move quire percep- 
tibly during rhe long exposure, and irs image upon rhe 
will be. nor a dor, bur a stnak. which can 
g zed ar a glance. S m times bus many ;:s seven 
planets thus "show up" upon a single plate, — Id Hies 
- well - I oi» : but a few night-' — rvarion 

will usually furnish data from which rhe orbits 

mputed with suffieienr accuracy ro decide all doubrful 

questions. Max Wolf of Heidelberg, who firsr introduced 

rhe method, and Charlois of Nice, have been especially 

—tul in this kind of asreroid-hunring. Among rhe 

shioned planer-himrers Palisa of Vienna rook rhe h 



J 



THE ASTEROIDS 227 

as the discoverer of 71 ; the late Dr. Peters of Clinton, 
X.Y., stood second with 48. 

261. Their Orbits. — The mean distances of the different 
asteroids from the sun differ pretty widely, and the periods, 
of course, correspond. Eros, (433), has by far the smallest 
orbit, its mean distance from the sun being only 1.46 
(135,500000 miles), and its period 648, even less than that of 
Mars. The next in proximity to the sun is Adalberta, (§»), 
with a mean distance of 194,000000 miles, and a period 
of three years and three days. Thule, (279), is the most 
remote, with a mean distance of 4.30 (400,000000 miles) 
and a period only ten days less than nine years. 

The inclinations of the orbits to the ecliptic average 
nearly 8°. The orbit of Pallas, ©, is inclined at an angle 
of 35°, and seven others exceed 25°. The eccentricity of 
the orbits is very large in many cases. JEthra, (132), (one 
of the eight or nine that are " adrift," i.e., that have been 
lost sight of and not observed for a number of years) has 
the largest eccentricity (0.38), and ten others have an 
eccentricity exceeding 0.30. It should be noted that the 
orbits of these planets are subject to very great disturb- 
ances from the attraction of Jupiter, and this makes the 
calculation of their motions much more laborious than 
that of the larger planets. Very few of them, therefore, 
are followed up closely; only those that for some reason 
or other possess a special interest at some given time. 

262. The Bodies themselves. — The four first discovered, 
and one or two others, when examined with a powerful 
telescope, show disks that are perceptible, but too small 
for satisfactory measurement with ordinary telescopes. 
By photometric observations, assuming — what is by no 



228 



LESSONS IN ASTRONOMY 



means certain — that their albedo is about the same as that 
of Mars, it has been estimated that Vesta, the brightest, 
has a diameter of about 320 miles, and that the other three 
of the first four may be two-thirds as large. In 1895, 
however, Mr. Barnard of the Lick Observatory measured 
the diameters of Ceres, Pallas, and Vesta, micrometrically, 
and obtained results that differ from these very widely, 
and should probably be preferred. He finds Ceres to be 
the largest, with a diameter of 488 miles. For Pallas, 
Vesta, and Juno he gets diameters of 304, 248, and 
118 miles, respectively. None of the rest can well exceed 
100 miles; and the more newly discovered ones, which 
are just fairly visible in a telescope with an aperture of 
10 or 12 inches, cannot be many times larger than the 
moons of Mars, — say from 10 to 20 miles in diameter. 

As to the individual masses and densities, we have no 
certain knowledge. 

Assuming the correctness of Barnard's measures, and that the 
density of Ceres is about the same as that of the rocks which com- 
pose the earth's crust, her mass may be as great as q-^qq that of the 
earth. If so, gravity on her surface would be about -i- of gravity 
here, so that a body would fall about seven inches in the first second. 
Of course, on the smaller asteroids it would be much less. 



From the perturbations of Mars, Leverrier has estimated 
that the aggregate mass of the whole swarm cannot exceed 
one-fourth the mass of the earth, — something more than 
double that of Mars ; a more recent calculation by Ravene 
puts the limit as low as one per cent. 

The united mass of those at present known would make only a 
small fraction of such a body, — hardly a thousandth of it ; probably, 
however, those still undiscovered are very numerous. 



THE ASTEROIDS 229 

262*. Eros. — The most interesting of these little bodies 
from the astronomical point of view is Eros, (433), dis- 
covered by Witt at Berlin in 1898. 

Its mean distance and period, as already stated, are less 
than those of Mars, but the eccentricity of its orbit (0.22) 
is such that it goes far outside the Martial orbit at aphe- 
lion, while at perihelion it comes within 13,500000 miles 
of the orbit of the earth. This is only a little more than 
half the nearest approach of Venus, and gives the planet 
immense importance as a means of determining the solar 
parallax by the method explained in Sec. 468 of the 
Manual. But it is only when the perihelion passage 
occurs about January 20 that the earth is rightly situated 
to utilize the conditions, and unfortunately these close 
approaches are very rare. 

One occurred in 1894, before the discovery of the 
planet; the next will be in 1938. But in the winter of 
1900-1901 the conditions were better than they will be 
again for thirty years, the nearest approach being within 
about 30,000000 miles. An enormous number of obser- 
vations were made, both visual and photographic, the 
results of which will require some years for their complete 
discussion. 

The planet's inclination is about 11°, so that at the 
time of a close opposition it moves among the stars nearly 
from north to south, instead of retrograding from east to 
west like other planets. 

It is very small, probably less than twenty miles in 
diameter, and seldom visible except in great telescopes ; at 
its close approaches, however, it may become nearly bright 
enough to be visible by the naked eye. 



230 LESSONS IN ASTRONOMY 

In certain positions relative to the earth there is a 
marked periodic variation of its light, and from this 
Director Pickering of Harvard has deduced by photomet- 
ric observations a rotation period of about 5i hours. One 
or two other asteroids are suspected of similar behavior, 
and are also under observation. 

263. Origin. — As to this we can only speculate. It is 
hardly possible to doubt, however, that this swarm of little 
rocks in some way represents a single planet of the " ter- 
restrial " group. A commonly accepted view is that the 
material, which, according to the nebular hypothesis, once 
formed a ring (like one of the rings of Saturn), and ought 
to have collected to make a single planet, has failed to 
be so united ; and the failure is ascribed to the perturba- 
tions produced by the next neighbor, the giant Jupiter, 
whose powerful attraction is supposed to have torn the 
ring to pieces, and thus prevented its normal development 
into a planet. 

Another view is that the asteroids may be fragments of 
an exploded planet. If so, there must have been not one 
but many explosions, — first of the original body, and then 
of the separate pieces ; for it is demonstrable that no single 
explosion could account for the present tangle of orbits. 

INTRAMERCURIAN PLANETS AND THE ZODIACAL 

LIGHT 

264. Intramercurian Planets. — It is very possible, indeed not 
improbable, that there is a considerable quantity of matter circu- 
lating around the sun inside the orbit of Mercury. It has been 
somewhat persistently supposed that this intramercurian matter is 
concentrated into one, or possibly two, planets of considerable size, 



HIE ZODIACAL LIGHT 231 

and such a planet has several times been reported as discovered, and 
has even been named Vulcan. The supposed discoveries have never 
been confirmed, however, and the careful observations of total solar 
eclipses during the past ten years make it practically certain that 
then* is no " Vulcan." Possibly, however, there is a family of intra- 
mercurian asteroids; but they must be very minute or some of them 
would certainly have been found either during eclipses or crossing 
the sun's disk ; a planet as much as 200 miles in diameter could 
hardly have escaped discovery. For the coming eclipse of 1005 
an elaborate photographic campaign is being arranged in order, 
if possible, to detect some of these hypothetical " pianettes," as 
Miss Clerke calls such bodies. 

265. The Zodiacal Light. — This is a faint, ill-defined 
pyramidal beam of light extending from the sun both ways 
along the ecliptic. In the evening it is best seen in the 
early spring, and in our latitude then extends about 90° 
eastward from the sun ; in the tropics it is said that it can 
be followed quite across the sky. The region near the sun 
is fairly bright and even conspicuous, but the more distant 
portions are extremely faint and can be observed only in 
places where there is no illumination of the air by artificial 
lights. At the point opposite the sun in the heavens there 
is also a faint patch of light, ten degrees or so in diameter, 
known as the Gregensehein, or " counter glow." 

The spectrum of the zodiacal light is a simple, con- 
tinuous spectrum without markings of any kind, so far 
as can be observed. We emphasize this because of late it 
is often mistakenly stated that the bright line which char- 
acterizes the spectrum of the Aurora Borealis appears in 
the spectrum of the zodiacal light. 

The cause of the phenomenon is not certainly known. 
Some imagine that the zodiacal light is only an extension 



232 LESSONS IN ASTRONOMY 

of the solar corona (whatever that may be), which is not 
perhaps unlikely; but on the whole the more prevalent 
opinion seems to be that it is due to sunlight reflected from 
myriads of small meteoric bodies circling around the sun, 
nearly in the plane of the ecliptic, thus forming a thin flat 
sheet (something like one of Saturn's rings), which extends 
far beyond the orbit of the earth. As to the Gegenschein, 
it is generally ascribed to a brightening up of the little 
bodies when they come opposite to the sun, similar to the 
moon's great increase of brightness at the full (Sec. 149). 

THE MAJOR PLANETS — JUPITER, URANUS, AND 
NEPTUNE 

JUPITER 

266. Jupiter, the nearest of the major planets, stands 
next to Venus in the order of brilliance among the heavenly 
bodies, being fully five or six times as bright as Sirius, and 
decidedly superior to Mars, even when Mars is nearest. It 
is not, like Venus, confined to the twilight sky, but at the 
time of opposition dominates the heavens all night long. 

Its orbit presents no marked peculiarities. The mean 
distance of the planet from the sun is a little more than 
five astronomical units (483,000000 miles), and the eccen- 
tricity of the orbit is not quite ^, so that the actual dis- 
tance ranges about 21,000000 miles each side of the mean. 
At an average opposition the planet's distance from the 
earth is about 390,000000 miles, while at conjunction it is 
distant about 580,000000. 

The inclination of its orbit to the ecliptic is only 1° 19'. 
Its sidereal period is 11.86 years, and the synodic is 399 



JUPITER 233 

days (a figure easily remembered), a little more than a year 
and a month ; i.e., each year Jupiter comes to opposition a 
month and four days later than in the preceding year. 

267. Dimensions, Mass, Density, etc. — The planet's 
apparent diameter varies from 50" to 32", according to its 
distance from the earth. The disk, however, is distinctly 
oval, so that while the equatorial diameter is nearly 90,000 
miles, the polar diameter is only 84,200. The mean diameter 
(see Sec. 112) is 88,000 miles, a little more than eleven 
times that of the earth. 

These values are from recent measures by Barnard and See, and 
quite possibly need correction for irradiation. They are notably 
larger than those determined by earlier observers with a different 
kind of micrometer and given in Table II of the Appendix. Very 
likely the truth is intermediate. 

Its surface, therefore, is 122, and its volume or bulk 1355, 
times that of the earth. It is by far the largest of all the 
planets, — larger, in fact, than all the rest united. 

Its mass is very accurately known, both by means of 
its satellites and from the perturbations it produces upon 
certain asteroids. It is j-$jg of the sun's mass, or about 
316 times that of the earth. 

Comparing this with its volume, we find its mean density 
to be 0.24, i.e., less than one-fourth the density of the 
earth and almost precisely the same as that of the sun. 
Its surface gravity is about two and two-thirds times that 
of the earth, but varies nearly twenty per cent between the 
equator and poles of the planet on account of the rapid 
rotation. 

268. General Telescopic Aspect, Albedo, etc. — In a small 
telescope the planet is a fine object ; for a magnifying 



234 LESSONS IN ASTRONOMY 

power of only 60 makes its apparent diameter, even when 
remotest, equal to that of the moon. With a large instru- 
ment and a magnifying power of 200 or 300 it is magnifi- 
cent, the disk being covered with an infinite variety of 
detail, interesting in outline and rich in color, changing 
continually as the planet turns on its axis. For the most 
part, the markings are arranged in " belts" parallel to the 
planet's equator, as shown in Fig. 64. 

This is from an admirable drawing made in 1889 by the late 
lamented Keeler, and still continues to be an excellent represen- 
tation of the planet, wanting only the varied colors to make it 
perfect, 

Near the limb the light is less brilliant than in the center 
of the disk, and the belts there fade out. The planet shows 
no perceptible phases, but the edge which is turned away 
from the sun is usually sensibly darker than the other. 
According to Zollner, the mean albedo of the planet is 0.62, 
which is extremely high, that of white paper being only 
0.78. The question has been raised whether Jupiter is 
not to some extent self-luminous, but there is no proof, and 
little probability, that such is the case. 

269. Atmosphere and Spectrum. — The planet's atmos- 
phere must be very extensive. The forms which we see 
with the telescope are all evidently atmospheric. In fact, 
the low mean density of the planet makes it very doubtful 
whether there is anything solid about it anywhere, — 
whether it is anything more than a ball of fluid, overlaid 
by cloud and vapor. 

The spectrum of the planet differs less from that of mere 
reflected sunlight than might have been expected, showing 
that the light is not obliged to penetrate the atmosphere 




Fig. 64. — Jupiter 

After drawings by Keeler, at Lick Observatory 

235 



236 LESSONS IN ASTRONOMY 

to any great depth before it encounters the reflecting 
envelope of cloud. There are, however, certain unex- 
plained dark shadings in the red and orange parts of the 
spectrum that are probably due to the planet's atmosphere, 
and seem to be identical in position with certain bands 
which, in the spectra of Uranus and Neptune, are much 
more intense. 

270. Rotation. — Jupiter rotates on its axis more swiftly 
than any other of the planets. Its sidereal day has a length 
of about 9 h 55 m ; but the time can be given only approxi- 
mately, because different results are obtained from differ- 
ent spots, according to their nature and their distance 
from the equator, — the differences amounting to six or 
seven minutes as determined by spots of different char- 
acter and in different latitudes. White spots generally make 
the circuit quicker than dark spots near them. 

In consequence of the swift rotation, the planet's oblate- 
ness, or " polar compression," is quite noticeable, — about ^ . 
The inclination of the planet's equator to its orbit is only 
3°, so that there can be no well-marked seasons on the 
planet due to such causes as produce our own seasons. 

271. Physical Condition. — This is obviously very dif- 
ferent from that of the earth or Mars. No permanent 
markings are found upon the disk, though occasionally 
there are some which may be called " sub-permanent," as, 
for instance, the great red spot, shown in Fig. 64. This 
was first noticed in 1878, became extremely conspicuous 
for several years, and still (1903) remains visible as a 
faded ghost of itself. Were it not that during the first 
eight years of its visibility it changed the length of its 
apparent rotation by about six seconds (from 9 h 55 n, 34 s .9 to 



JUPITER 237 

9 h 55 m 40 8 .2), we might suppose it permanently attached 
to the planet's surface, and evidence of a coherent mass 
underneath. As it is, opinion is divided on this point; 
the phenomenon is as puzzling as the canals of Mars. 

Many things in the planet's appearance indicate a high 
temperature, as, for instance, the abundance of clouds and 
the swiftness of their transformations ; and since on Jupi- 
ter the solar light and heat are only -^ as intense as here, 
we are forced to conclude that it gets very little of its 
heat from the sun, but is probably hot on its own account, 
and for the same reason that the sun is hot, viz., as the 
result of a process of condensation. In short, it appears 
very probable that the planet is a sort of semi-sun, — hot, 
though not so hot as to be sensibly self-luminous. 

272. Satellites. — Jupiter has five satellites, four of 
them large and easily seen with a very small telescope, 
while m the fifth, discovered by Barnard in 1892, is 
extremely small and visible only in the largest instru- 
ments. 

The four large satellites were the first heavenly bodies 
ever discovered. Galileo found them in January, 1610, 
within a few weeks after the invention of his telescope. 

These are now usually known as the first, second, etc., 
in the order of their distance from the planet. The dis- 
tances range from 262,000 to 1,169000 miles, being 
respectively 6, 9, 15, and 26 radii of the planet (nearly). 
Their sidereal periods range from 42 hours to 16f days. 
Their orbits are sensibly circular and lie very nearly in 
the plane of the equator. The third satellite is much the 
largest, having a diameter of about 3600 miles, while the 
others are between 2000 and 3000. 



238 LESSONS IN ASTRONOMY 

For some reason, the fourth satellite is a very dark-complexioned 
body, so that when it crosses the planet's disk it looks like a black 
spot, hardly distinguishable from its own shadow ; the others under 
similar circumstances appear bright, dark, or invisible, according to 
the brightness of the part of the planet which happens to forni the 
background. In the case of the fourth satellite a certain regularity 
in its changes of brightness suggests that it probably follows the 
example of our moon in always keeping the same face towards 
the planet, and Douglass from the Flagstaff Observatory, in 1897, 
announced a similar behavior of the third. Professor W. H. Pick- 
ering reports that they show certain curious and regularly recurring 
changes of form, which indicate that they are not solid masses, but 
whirling clouds or swarms of minute particles. Barnard, howev T er, 
and other observers of the highest authority, fail to recognize any 
departure from roundness. 

The fifth satellite is at a distance of about 112,500 miles, and its 
period of revolution is ll h 57 m 22 s .6. Its diameter is probably less 
than 100 miles. 

273. Eclipses and Transits. — The orbits of the satellites 
are so nearly in the plane of the planet's orbit that with 
the exception of the fourth, which escapes about half the 
time, they are eclipsed at every revolution. Ordinarily 
we see only the beginning or the end of an eclipse ; but 
when the planet is very near quadrature the shadow pro- 
jects so far to one side that the whole eclipse of every 
satellite, except the first, takes place clear of the disk, 
and both the disappearance and reappearance can be 
observed. At opposition neither is visible. 

Two important uses have been made of these eclipses : 
they have been employed for the determination of longi- 
tude, and they furnish the means of ascertaining the time 
required by light to traverse the space between the earth and 
the sun. (See Appendix, Sees. 431-434.) 



SATURN 239 



SATURN 



274. This is the most remote of the planets known to 
the ancients. It appears as a star of the first magnitude 
(outshining all of them, indeed, except Sirius) with a 
steady, yellowish light, not varying much in appearance 
from month to month, though in the course of fifteen 
years it alternately gains and loses nearly fifty per cent 
of its brightness with the changing phases of its rings; 
for it is unique among the heavenly bodies, a great globe 
attended by eight satellites and surrounded by a system of 
rings which has no counterpart elsewhere in the universe, 
so far as known. 

Its mean distance from the sun is about 9i astronomical 
units, or 886,000000 miles; but the distance varies over 
100,000000 miles on account of the considerable eccen- 
tricity of the orbit (0.056). Its least distance from the 
earth is about 774,000000 miles, the greatest about 
1028,000000 N The inclinauon of the orbit to the ecliptic 
is 2J°. The sidereal period is about 29i years, the synodic 
period being 378 days, or nearly a year and a fortnight. 

'275. Dimensions, Mass, etc. — The apparent mean 
diameter of the planet varies according to the distance, 
from 14" to 20". The planet is more flattened at the 
poles than any other (nearly J^), so that while the equa- 
torial diameter is about 75,000 miles, the polar is only 
68,000; the mean diameter (Sec. 112) being not quite 
73,000,* — a little more than nine times that of the earth. 
Its surface is about 84 times that of the earth, and its 
volume 770 times. Its mass is found (by means of its 

1 Barnard's measures give a diameter about 1000 miles larger. 



240 LESSONS IN ASTRONOMY 

satellites) to be 95 times that of the earth, so that its 
mean density comes out only one-eighth that of the earth, 
— actually less than that of water/ It is by far the least 
dense of all the planetary family. 

Its mean superficial gravity is about 1.2 times as great 
as gravity upon the earth, varying, however, nearly twenty- 
five per cent between the equator and the pole, so that at 
the planet's equator it is practically the same as upon the 
earth. It rotates on its axis in about 10 ll 14 ,n , but different 
spots give various results, as in the case of Jupiter. 

The equator of the planet is inclined about 27° to the 
plane of its orbit — about 28° to the ecliptic. 

276. Surface, Albedo, Spectrum. — The disk of the 
planet, like that of Jupiter, is shaded at the edge, and, like 
Jupiter, it shows a number of belts arranged parallel to 
the equator. The equatorial belt is very bright, and is 
often of a delicate pinkish tinge. The belts in higher 
latitudes are comparatively faint and narrow, while just at 
the pole there is usually a cap of olive green (see Fig. 65). 

Zollner makes the mean albedo of the planet 0.52, about 
the same as that of Venus. 

The planet's Spectrum is substantially like that of 
Jupiter, but the dark bands are more pronounced. These 
bands, however, do not appear in the spectrum of the ring, 
which probably has very little atmosphere. As to its phys- 
ical condition and constitution, the planet is probably much 
like Jupiter, though it does not seem to be tk boiling" 
quite so vigorously. 

277. The Rings. — The most remarkable peculiarity of 
the planet is its ring system. The globe is surrounded by 
three thin, flat, concentric rings, like circular disks of 




Fig. 65. — Saturn 
After Proctor 



241 



242 LESSONS IN ASTRONOMY 

paper pierced through the center. They are generally 
referred to as A, i>\ and C, A being the exterior one. 

Galileo half discovered them in 1610 ; i.e., he saw with his little 
telescope two appendages, one on each side of the planet; bnt he 
could make nothing of them, and after a while he lost them. The 
problem remained unsolved for nearly fifty years, until Huyghens 
explained the mystery in 1655. Twenty years later D. Cassini dis- 
covered that the ring is double, i.e., composed of two concentric 
rings, with a dark line of separation between them, and in 1850, 
Bond of Cambridge (U.S.) discovered the third " dusky " or " gauze'" 
ring between the principal ring and the planet. (It was discovered 
a fortnight later, independently, by Dawes in England.) 

The outer ring, A, has a diameter of about 173,000 
miles and a width of not quite 1200. Cassini's division 
is about 2000 miles wide ; the ring B, which is much 
the broadest of the three, is about 17,000. The semi- 
transparent ring, C, has a width of about 10,000 miles, 
leaving a clear space of from 8000 to 9000 miles hi width 
between the planet's equator and its inner edge. The 
thickness of the rings is extremely small, — probably not 
over 100 miles, as proved by the appearance presented, 
when once in 15 years we view them edgewise. 

The recent researches of H. Struve show that the 
mass of the rings and their mean density are also sur- 
prisingly small, — so small that the rings exert hardly 
more influence on the motion of the satellites than if they 
were composed of " immaterial light," to use his own expres- 
sion. A very recent discussion by Professor Hall indi- 
cates, however, that the mass, though certainly extremely 
small, is by no means insensible, being about ^^ of the 
planet's mass, and not very much less than that of Titan, 
the largest satellite. 



SATURN 243 

278. Phases of the Rings. — The plane of the rings 
coincides with the plane of the planet's equator, and is 
inclined about 28° to the ecliptic. It, of course, remains 
parallel to itself at all times. Twice in a revolution of 
the planet, therefore, this plane sweeps across the orbit 
of the earth (too small to be shown in Fig. 66), occu- 
pying nearly a year in so doing ; and whenever the plane 
passes between the earth and the sun the dark side of 
the ring is towards us and the edge alone is visible, 




Fig. bo\ — The Phases of Saturn's Kings 

as when the planet is at 1 or 2 ; when it is at the inter- 
mediate points, 3 and 4, the rings present their widest 
opening. 

When the ring is exactly edgewise towards us, only the largest 
telescopes can see it, like a fine needle of light piercing the planet's 
ball, as in the uppermost engraving of Fig. 65. It becomes obvious 
at such times that the thickness of the rings is not uniform, since 
considerable irregularities appear upon the line of light at different 
points. The last period of disappearance was in 1892 ; the next 
will be in 1907. 



244 LESSONS IN ASTRONOMY 

279. Structure of the Rings. — It is now universally 
admitted that they are not continuous sheets, either solid 
or liquid, but mere swarms of separate particles, each par- 
ticle pursuing its own independent orbit around the planet, 
though all moving nearly in a common plane. 

The idea was first suggested by J. Cassini in 1715, but was lost 
sight of until again brought into notice by Bond in 1850. A little 
later Peiree proved from mechanical considerations that the rings 
could not be solid ; and not long after, Maxwell showed that they 
could not be " continuous sheets " of any kind, either solid or liquid, 
but might be composed of separate particles moving independently. 
More recently M tiller and Seeliger have shown from photometric 
observations that the variations in the brightness of the ring corre- 
spond to this "meteoric theory " ; and still more recently (in 1895) 
Keeler demonstrated, by a most beautiful and delicate spectroscopic 
observation, that the outer edge of the ring in its rotation really 
moves more slowly than the inner, just as the theory requires. 

It remains uncertain whether the rings constitute a system that 
is permanently stable, or whether they are liable ultimately to be 
broken up and disappear. 

280. Satellites. — Saturn has eight (possibly nine) of 
these attendants, the largest of which was discovered by 
Huyghens in 1655. It looks like a star of the ninth 
magnitude, and is easily seen with a three-inch telescope. 
The smallest one, the seventh in order of distance from 
the planet, was discovered by Bond at Cambridge (U.S.), 
in 1848. 

Since the order of discovery does not agree with that of distance, 
it has been found convenient to designate them by the names 
assigned by Sir John Herschel, as follows, beginning with the 
most remote, viz. : Iapgtus (Hyperion), Titan, Rhea, Dione, Tethys ; 
Enceladus, Mimas. (The name Hyperion wa$ not given by Herschel, 
but interpolated after its discovery by Bond.) 



LJ URANUS 245 

The range of the system is enormous. Iapetus has a distance of 
2,225000 miles, with a period of 79 days, — nearly as long as that of 
Mercury. On the western side of the plaiiet this satellite is always 
much brighter than upon the eastern, showing that, like our own 
moon, it keeps the same face tow T ards its primary. 

Titan, as its name suggests, is by far the largest. Its distance is 
about 770,000 miles and its period a little less than 16 days. It is 
probably 3000 or 4000 miles in diameter, and, according to Stone, 
its mass is ^Vo of Saturn's, or about double that of our moon. 
The orbit of Iapetus is inclined nearly 10° to the plane of the 
rings, but all of the other satellites move almost exactly in their 
plane, and all the five inner ones in orbits nearly circular. In 1899 
W. H. Pickering announced the discovery of an extremely small 
ninth satellite on photographs made at Arequipa the preceding year. 
The data were insufficient to determine its orbit, but indicate that 
its distance from the planet must be at least six or seven million 
miles. He proposes for it the name of Phoebe. 

Thus far, however, the discovery lacks confirmation. 



URANUS 

281. Uranus (not U-ra/nus) was the first planet ever 
" discovered," and the discovery created great excitement 
and brought the highest honors to the astronomer. It was 
found accidentally by the elder Herschel on March 13, 
1781, while " sweeping" for interesting objects with a 
seven-inch reflector of his own construction. He recog- 
nized it at once by its disk as something different from a 
star, but supposed it to be a peculiar sort of comet, and 
its planetary character was not demonstrated until nearly 
a year had passed. It is easily visible to a good eye as 
a star of the sixth magnitude. 

Its mean distance from the sun is about 19 times that of 
the earth, or about 1800,000000 miles, and the eccentricity 



246 LESSONS IN ASTRONOMY 

of its orbit is about the same as that of Jupiter's. The 
inclination of the orbit to the ecliptic is very slight, — 
only 46'. The sidereal period is 84 years, and the synodic 
369i days. 

In the telescope it shows a greenish disk about 4" in 
diameter, which corresponds to a real diameter of about 
32,000 x miles. This makes its bulk about 66 times that 
of the earth. The planet's mass is found from its satel- 
lites to be about 14.6 times that of the earth ; its density, 
therefore, is 0.22, — about the same as that of Jupiter and 
the sun. 

The albedo of the planet, according to Zollner, is very 
high, 0.64, — even a little above that of Jupiter. The 
spectrum exhibits intense dark bands in the red, due to 
some unidentified substance in the planet's atmosphere. 
These bands explain the marked greenish tint of the 
planet's light. The atmosphere is probably dense. 

The disk is obviously oval, with an ellipticity of about 
Y 1 ^. There are no clear markings upon it, but there seem 
to be faint traces of something like belts. No spots are 
visible from which to determine the planet's diurnal 
rotation. Probably, however, it is rapid. 

282. Satellites. — The planet has four satellites, — 
Ariel, Umbriel, Titania, and Oberon, Ariel being the 
nearest to the planet. 

The two brightest, Oberon and Titania, were discovered by Sir 
William Herschel a few years after his discovery of the planet ; Ariel 
and Umbriel, by Lassell in 1851. 

1 See makes its diameter only 28,500 miles, which correspondingly 
reduces its bulk to 47 times that of the earth, and increases its density 
to 0.31. 



NEPTUNE 247 

They are among the smallest bodies in the solar system 
and the most difficult to see. 

Their orbits are sensibly circular, and all lie in one 
plane, which ought to be, and probably is, coincident with 
the plane of the planet's equator. 

They are very close packed also, Oberon having a distance of only 
375,000 miles and a period of 13 d ll h , while Ariel has a period of 
2 d 12 h at a distance of 120,000 miles. Titania, the largest and 
brightest of them, has a distance of 280,000 miles, somewhat 
greater than that of the moon from the earth, with a period of 
8 d 17 h . 

The most remarkable thing about this system remains to 
be mentioned. The plane of their orbits is inclined 82°. 2, 
or almost perpendicularly, to the plane of the ecliptic, and 
in that plane they revolve backwards. 



NEPTUNE 

283. Discovery. — The discovery of this planet is con- 
sidered the greatest triumph of mathematical astronomy. 
Uranus failed to move precisely in the path computed for 
it, and was misguided by some unknown influence to an 
extent which could almost be seen with the naked eye. 
The difference between the actual and computed places in 
1845 was the " intolerable quantity " of nearly two minutes 
of arc. 

This is a little more than half the distance between the two prin- 
cipal components of the double-double star, Epsilon Lyrse, the north- 
ern one of the two little stars which form the small equilateral 
triangle with Vega (Sees. 67 and 375). A very sharp eye detects 
the duplicity of Epsilon without the aid of a telescope. 



248 LESSONS IN ASTRONOMY 

One might think that such a minute discrepancy between 
observation and theory was hardly worth minding, and that 
to consider it " intolerable" was putting the case very 
strongly. But just these minute discrepancies supplied 
the data which were found sufficient for calculating the 
position of a great unknown world, and bringing it to 
light. As the result of a most skillful and laborious inves- 
tigation, Leverrier (born 1811, died 1877) wrote to Galle 1 
in substance : 

" Direct your telescope to a point on the ecliptic in the constella- 
tion of Aquarius, in longitude 326°, and you will find within a degree 
of that place a new planet, looking like a star of about the ninth 
magnitude, and having a perceptible disk." 

The planet was found at Berlin on the night of Sept. 23, 
1846, in exact accordance with this prediction, within 
half an hour after the astronomers began looking for it 
and within 52' of the precise point that Leverrier had 
indicated. 

We cannot here take the space for an historical statement, further 
than to say that the English Adams fairly divides with Leverrier the 
credit for the mathematical discovery of the planet, having solved 
the problem and deduced the planet's approximate place even earlier 
than his competitor. The planet was being searched for in England 
at the time it was found in Germany. In fact, it had already been 
observed, and the discovery would necessarily have followed in a few 
weeks, upon the reduction of the observations. 

284. Error of the Computed Orbit. — Both Adams and Leverrier, 
besides calculating the planet's position in the sky, had deduced ele- 
ments of its orbit and a value for its mass, which turned out to be 

1 Galle, long director of the observatory at Breslau, but now retired, 
is still living (1903), ninety years old, — the only survivor of all those 
connected with the great discovery. 



NEPTUNE 249 

seriously wrong, and certain high authorities have therefore charac- 
terized the discovery as a "happy accident." This is not so, how- 
ever. While the data and methods employed were not sufficient 
to determine the planet's orbit with accuracy, they were adequate 
to ascertain the planet's direction from the earth. The computers 
informed the observers ichere to point their telescopes, and this was all 
that was necessary for finding the planet. 

285. The Planet and its Orbit. — The planet's mean dis- 
tance from the sun is a little less than 2800,000000 miles 
(800,000000 miles nearer the sun than it should be accord- 
ing to Bode's law). The orbit is very nearly circular, its 
eccentricity being only 0.009. The inclination of the orbit 
is about If °. The period of the planet is about 164 years 
(instead of 217, as it should have been according to Lever- 
rier's computed orbit) and the orbital velocity is about 
3J miles per second. 

Neptune appears in the telescope as a small star of 
between the eighth and ninth magnitudes, absolutely 
invisible to the naked eye, though easily seen with a 
good opera-glass. Like Uranus, it shows a greenish disk, 
having an apparent diameter of about 2". 6. The real 
diameter of the planet is about 30,000* miles according 
to Struve, which makes its volume about 60 times that of 
the earth. 

Its mass, as determined by means of its satellite, is about 
18 times that of the earth, and its density 0.30. 

The planet's albedo, according to Zollner, is 0.46, — a 
trifle less than that of Saturn and Venus. 

There are no visible markings upon its surface, and 
nothing certain is known as to its rotation. 

1 33,000 according to Barnard. 



250 LESSONS IN ASTRONOMY 

The spectrum of the planet appears to be like that of 
Uranus, but of course is rather faint. 

It will be noticed that Uranus and Neptune form a " pair of 
twins," very much as the earth and Venus do, being almost alike in 
magnitude, density, and many other characteristics. 

286. Satellite. — Neptune has one satellite, discovered 
by Lassell within a month after the discovery of the planet 
itself. Its distance is about 222,000 miles, and its period 
52 d l h . Its orbit is inclined to the ecliptic at an angle of 
34° 48', and it moves backward in it from east to west, 
like the satellites of Uranus. From its brightness, as com- 
pared with that of Neptune itself, its diameter is estimated 
as about the same as that of our own moon. 

287. The Solar System as seen from Neptune. — At 
Neptune's distance the sun itself has an apparent diam- 
eter of only a little more than one minute of arc, — about 
the diameter of Venus when nearest us, and too small to 
be seen as a disk by the naked eye, if there are eyes on 
Neptune. The solar light and heat there are only r ^-^ of 
what we get at the earth. 

Still, we must not imagine that the Neptunian sunlight 
is feeble as compared with starlight, or even moonlight. 
Even at the distance of Neptune the sun gives a light 
nearly equal to 700 full moons. This is about 80 times 
the light of a standard candle at one meter's distance, and 
is abundant for all visual purposes. In fact, as seen from 
Neptune, the sun would look very like a large electric arc 
lamp at a distance of a few yards. 

288. Ultra-Neptunian Planets. — Perhaps the breaking down of 
Bode's law at Neptune may be regarded as an indication that the 






STABILITY OF SOLAR SYSTEM 251 

solar system terminates there, and that there is no remoter planet ; 
but of course it does not make it certain. If such a planet exists, it 
is sure to be found sooner or later, either by means of the disturb- 
ances it produces in the motion of Uranus and Neptune, or else by 
the methods of the asteroid hunters, — although its slow motion will 
render its discovery in that way difficult. Quite possibly such a dis- 
covery may come within a few years as a result of the photographic 
star-charting operations now in progress. 

288*. Stability of the Solar System. — It is an interesting and 
important question, once long and warmly discussed, whether the 
so-called " perturbations," which result from the mutual attractions 
of the planets, can ever seriously derange the system. It is now 
nearly a century since Laplace and Lagrange first demonstrated that 
they cannot. The system is stable in itself, all the planetary dis- 
turbances due to gravitation being either of such a character, or so 
limited in extent, that they can never produce any seriously harmful 
effects upon any of the larger planets, the earth included. 

It does not follow, however, that because the mutual attractions of 
the. planets are thus harmless, there may not be other causes which 
would act disastrously. Many such are conceivable, — such, for 
instance, as the retardation of the speed of the planets, which would 
be caused by the presence of a resisting medium in space, or by the 
encounter of the system with a sufficiently dense and extended cloud 
of meteors. 

But so far as we can now judge, the ultimate cooling of the sun 
(Sec. 193) is likely to extinguish life upon the planets long before 
the mechanical destruction of the system can occur from any such 
external causes. 

Note. — The values given in Table II of the Appendix are allowed to 
stand as in former editions, in order that their comparison with those 
given in the text may illustrate to the student the measure of uncertainty 
that still remains in such astronomical data. 



CHAPTER X 

COMETS AND METEORS 

The Number, Designation, and Orbits of Comets — Their Constituent Parts 
and Appearance — Their Spectra and Physical Constitution — Their Prob- 
able Origin — Remarkable Comets — Photography of Comets — Aerolites, 
their Fall and Characteristics — Shooting-Stars, Meteoric Showers — Con- 
nection between Comets and Meteors 

COMETS 

289. Comets, their Appearance and Number. — The 
word " comet " (derived from the Greek home) means a 
" hairy star." The appearance is that of a rounded cloud 
of luminous fog with a star shining through it, often 
accompanied by a long fan-shaped train, or " tail," of hazy 
light. They present themselves from time to time in the 
heavens, mostly when unexpected, move across the con- 
stellations in a path longer or shorter according to circum- 
stances, and remain visible for some weeks or months 
until they fade out and vanish in the distance. The large 
ones are magnificent objects, sometimes as bright as Venus 
and visible by day, with a head as large as the moon, and 
having a train which extends from the horizon to the 
zenith, and is really long enough to reach from the earth 
to the sun. Such comets are rare, however ; the majority 
are faint wisps of light, visible only with the telescope. 
Fig. 67 is a representation of Donati's comet of 1858, 
which was one of the finest ever seen. 

252 




Fig, 67. — Naked-Eye View of Donati's Comer, Oct 4. 1858 
Bond 



254 LESSONS IN ASTRONOMY 

In ancient times comets were always regarded with terror, as at 
least presaging evil, if not actively malignant, and the notion still 
survives in certain quarters, though the most careful research goes 
to prove that they exert upon the earth not the slightest perceptible 
influence of any kind. 

Thus far, up to the beginning of the new century, our 
lists contain 800 recorded appearances, not all, however, 
of different comets, for some (periodic) have been counted 
several times. About 400 were observed before the inven- 
tion of the telescope in 1609, and therefore must have 
been fairly bright. Of those observed since then, only a 
small proportion have been conspicuous to the naked eye, — 
perhaps one in five. The total number that visit the solar 
system must be enormous ; for there is seldom a time 
when one at least is not in sight, and even with the tele- 
scope we see only the few which come near the earth and 
are favorably situated for observation. 

290. Designation of Comets. — A remarkable comet gen- 
erally bears the name of its discoverer or of some one who 
has " acquired its ownership," so to speak, by some impor- 
tant research concerning it. Thus we have Halley's, 
Encke's, and Donati's comets. The ordinary telescopic 
comets are designated only by the year of discovery, with 
a letter indicating the order of discovery in that year, as 
comet "a, 1890" (the letter preceding the year) ; or, still 
again, with the year and a Roman numeral following and 
denoting the order of perihelion passage, as 1890-1, the 
latter method being the most used. In some cases a comet 
bears a double name, as the Lexell-Brooks comet (1889-V), 
which was investigated by Lexell in 1770, and discovered 
by Brooks on its recent return in 1889, 



COMETS 255 

291. Duration of Visibility and Brightness. — The great 
comet of 1811 was observed for seventeen months, and 
the little comet, known as 1889-1, for more than two 
years, — the longest period of visibility on record. On 
the other hand, the whole appearance sometimes lasts only 
a week or two. The average is probably not far from 
three months. 

As to brightness, comets differ widely. About one in 
five reaches the naked-eye limit, and a very few, say four 
or five in a century, are bright enough to be seen in the 
daytime. The great comet of 1882 was the last one so 
visible. 

292. Their Orbits. — A large majority of the comets move 
in orbits that are sensibly parabolas. (See Appendix, Sees. 
439-440.) A comet moving in such an orbit approaches 
the sun from an enormous distance, far beyond the limits 
of the solar system, sweeps once around the sun, and goes 
off, never to come back. The parabola does not return 
into itself and form a closed curve, like the circle and 
ellipse, but recedes to infinity. Of the nearly 400 orbits 
that have been computed, more than 300 appear to be of 
this kind. About 85 orbits are more or less distinctly 
elliptical, and about half a dozen are perhaps hyperbolas 
(see Appendix, Sec. 440) ; but the hyperbolas differ so 
slightly from parabolas that the hyperbolic character is not 
really certain in a single case. 

Comets which have elliptical orbits of course return at 
regular intervals. Of the apparently elliptical orbits, 
there are about a dozen to which computation assigns 
periods near to or exceeding 1000 years. These orbits 
approach parabolas so closely that their real character is 



256 



LESSONS IN ASTRONOMY 



still rather doubtful. About 75 comets, however, have 
orbits which are distinctly and certainly elliptical, and 
60 have periods of less than one hundred years. About 
20 of these have been actually observed at two or more 
returns to perihelion. As to the rest of them, some are 
now due within a few years, and some have probably been 
lost to observation, either like Bielas comet (Sec. 312), or 

by having their 
/«, orbits transformed 

by perturbations. 

293. The first 
comet ascertained to 
move in an elliptical 
orbit was that known 
as Halley's, with a 
period of about sev- 
enty-six years, its peri- 
odicity having been 
discovered by Halley 
in 1681. It has since 
been observed in 1759 
and 1835 and is ex- 
pected again about 
1911. The second of 
the periodic comets 
(in the order of dis- 
covery) is Encke's, with the shortest period known, — only three and 
one-half years. Its periodicity was discovered in 1819, though the 
comet itself had been observed several times before. Fig. 68 shows 
the orbits of a number of short-period comets (it would cause confu- 
sion to insert more of them) and also a part of the orbit of Halley's 
comet. These comets all have periods ranging from three and one- 
half to eight years, and it will be noticed that they all pass very near 
to the orbit of Jupiter. Moreover, each comet's orbit crosses that of 




Fig. 68. — Orbits of Short-Period Comets 



ORBITS OF COMETS 257 

Jupiter near one of its nodes, the node being marked by a short cross 
line on the comet's orbit. The fact is very significant, showing that 
these comets at times come very near to Jupiter, and it points to an 
almost certain connection between that planet and these bodies. 

294. Comet-Groups. — There are several instances in which a 
number of comets, certainly distinct, chase each other along almost 
exactly the same path, at an interval usually of a few months or 
years, though they sometimes appear simultaneously. The most 
remarkable of these " comet-groups " is that composed of the great 
comets of 1668, 1843, 1880, 1882, and 1887. It is, of course, nearly 
certain that the comets of such a " group " have a common origin. 

295. Perihelion Distance, etc. — Eight of the 300 come- 
tary orbits, thus far determined, approach the sun within 
less than 6,000000 miles, and four have a perihelion 
distance exceeding 200,000000. A single comet (that of 
1729) had a perihelion distance of more than four " astro- 
nomical units," or 375,000000 miles. It must have been 
an enormous one to be visible at all under the circum- 
stances. There may, of course, be any number of comets 
with still greater perihelion distances, because, as a rule, 
we are able to see only such as come reasonably near the 
earth, and this is probably only a small percentage of the 
total number that visit the sun. 

The inclinations of cometary orbits range all the way 
from zero to 90°. As regards the direction of motion, all 
the elliptical comets having periods of less than one 
hundred years move direct, i.e., from west to east, except 
Halley's comet and Tempel's comet of 1866. Other 
comets show no decided preponderance either way. 

296. Parabolic Comets are Visitors. — The fact that the 
orbits of most comets are sensibly parabolic, and that their 
planes have no evident relation to the ecliptic, indicates 



268 LESSONS IX ASTRONOMY 

(though it does nor absolutely prove) that these bodies do 
not in any proper sense belong to the solar system, but 
only visitors. Such comets come to us precisely as if 
they simply dropped towards the sun from an enormous 
distance among the stars : and they leave the system with 
a velocity which, if no force but the sun's attraction acts 
upon them, will carry them away to an infinite distance. 
or until they encounter the attraction of some other 
sun. Their motions are just what might be expected of 
ponderable masses moving among the stars under the 
law of gravitation. 

A slightly different view is advocated by some high authorities, 
and is perhaps m<: : - : able, — that these comets come from 
distance indeed, but not from among the stars. It may be that our 
solar system, in its journey through space (Sec. 342), is accompanied 
by outlying clouds of nebulous matter, and that these are the source 
: the Diets. It is argued that if this se the number 

of/ itsT old be much greater, because w^ should 

so many more comets than could overtake us. 

297. Origin of Periodic Comets. — But while the para- 
bolic comets are thus probably strangers and visitors, 
re is juesti n as to the periodic comets which move 
in elliptical orbits. Are we to regard them as native 
citizens, or only as naturalized foreigners, - i speak? 
It is evident that, somehow or other, many of them stand 
in peculiar relations to Jupiter. Saturn, and other plane 
indicated in Sec. 29 

All short-period comets (those which have | - ran- 

ging from three to eight years 38 very close to the orbit 
of Jupiter, and are now recognized and spoken of as Jupi- 
ter's " familv oi Is"; m< re than twenty are known at 



THE CAPTURE THEORY 259 

present. Similarly, Saturn is credited with two comets, 
and Uranus with two, one of them being Tempel's comet, 
which is closely connected with the November meteors and 
should have returned in 1900, but was not seen. Finally, 
Neptune has a family of six ; among them Halley's comet, 
and two others which have returned a second time to 
perihelion since 1880. 

298. The Capture Theory The generally accepted 

theory as to the origin of these u comet-families " is one 
first suggested by Laplace nearly one hundred years ago, — 
that the comets which compose them have been captured by 
the planet to which they stand related. A comet entering 
the system in a parabolic orbit and passing near a planet 
will be disturbed, — either accelerated or retarded. If it 
is accelerated, it is easy to prove that the original para- 
bolic orbit will be changed to an hyperbola, and the 
comet will never be seen again, but will pass out of the 
system forever; but if it is retarded, the orbit becomes 
elliptical, and the comet will revolve around the sun (not 
around the capturing planet), returning at each successive 
revolution to the place where it was first disturbed. 

But this is not the end. After a certain number of 
revolutions, the planet and the comet will come together 
a second time at or near the place where they met before. 
The result may then be an acceleration which will send 
the comet out of the system finally ; but it is an even 
chance at least that it may be a second retardation and 
that the orbit and period may thus be further diminished ; 
and this may happen over and over again, until the comet's 
orbit falls so far inside that of the planet that there is no 
further disturbance to speak of. 



260 LESSONS IN ASTRONOMY 

Given time enough and comets enough, and the result 
would inevitably be such a comet-family as really exists. 
Its membership can hardly be permanent, however ; sooner 
or later, if not first disintegrated, each captured comet will 
almost certainly again encounter its captor under such 
circumstances as to be thrown out of the system, never 
to return. 

299. The Lexell-Brooks Comet — The " capture theory " 
has recently received an interesting illustration in the case 
of a little comet, 1889- V, discovered by Mr. Brooks of 
Geneva, N.Y., in July, 1889. It was soon found to be 
moving with a period of about seven years, in an elliptical 
orbit which passes very near to that of Jupiter. (We 
remark in passing that this comet, in August, divided into 
four fragments ; see Sec. 314.) On investigating the orbit 
more carefully, Dr. S. C. Chandler of Cambridge (U.S.) 
discovered that, in 1886, the comet and the planet had 
been close together for some months, and that as a conse- 
quence the comet's orbit must have been greatly changed, 
the previous orbit having been a much larger one with a 
probable period of nearly twenty-seven years. 

Now, in 1770, a famous comet appeared, which was 
bright, came very near the earth, and, according to Lexell's 
calculations, was then moving in an orbit with a period of 
only five and a half years, — the first instance of a short- 
period comet on record ; but it was never seen again. The 
calculations of Laplace, and later of Leverrier, showed that, 
in 1779, it must have passed very near to Jupiter and 
been thrown into an orbit too large to allow it to be seen 
from the earth ; also that the period might probably be 
about twenty-seven years. This would bring it very near 



CONSTITUTION OF COMETS 261 

to Jupiter again in 1886, and it was natural, therefore, for 
Dr. Chandler to infer the probable identity of the two 
comets, — a conclusion for a time generally accepted. 
Subsequent calculations by the late Dr. J. L. Poor of 
Baltimore threw doubt upon it, however, and the obser- 
vations made during the return of the comet in 1896 make 
it on the whole more likely that Brooks's comet is not iden- 
tical with Lexell's, but very probably a member of the same 
comet-group (Sec. 294). Dr. Poor found that the comet, 
in 1886, passed between Jupiter and the orbit of its first 
satellite within about 200,000 miles of the planet's surface, 
which accounts for its separation into four parts. 

PHYSICAL CONSTITUTION OF COMETS 

300. Constituent Parts of a Comet. — (a) The essential 
part of a comet — that which is always present and gives 
the comet its name — is the coma, or nebulosity, a hazy 
cloud of faintly luminous transparent matter. 

(b) Next, we have the nucleus, which, however, is want- 
ing in many comets, and makes its appearance only as the 
comet comes near the sun. It is a bright, more or less 
starlike point near the center of the comet. In some 
cases it is double, or even multiple. 

(c) The tail, or train, is a stream of light which com- 
monly accompanies a bright comet and is sometimes pres- 
ent even with a telescopic one. As the comet approaches 
the sun the tail follows it, but as the comet moves away 
from the sun it precedes. It is always, speaking broadly, 
directed away from the sun, though its precise form and 
position are determined partly by the comet's motion. 



262 LESSONS IN ASTRONOMY 

It is practically certain that it consists of extremely rarefied 
matter, which is thrown off by the comet and powerfully 
repelled by the sun. 

It certainly is not — like the smoke of a locomotive or train of a 
meteor — simply left behind by the comet, because as the comet is 
receding from the sun the tail goes before it, as has been said. 

(d) Jets and Envelopes. The head of a comet is often 
veined by short jets of light, which appear to be spurted 
out from the nucleus ; and sometimes the nucleus throws 
off a series of concentric envelopes like hollow shells, one 
within the other. These phenomena, however, are seldom 
observed in telescopic comets. 

301. Dimensions of Comets. — The volume, or bulk, of a 
comet is often enormous, — almost inconceivably so, if the 
tail is included in the estimate. The head, as a rule, is 
from 40,000 to 50,000 miles in diameter (comets less than 
10,000 miles in diameter would stand little chance of dis- 
covery). Comets exceeding 150,000 miles are rather rare, 
though there are several on record. 

The comet of 1811 at one time had a diameter of fully 1,200000 
miles, — forty per cent larger than that of the sun. The head of the 
comet of 1680 was 600,000 miles in diameter, and that of Donati's 
comet of 1858 about 250,000. Holmes's comet (1892) exceeded 
800,000. 

The diameter of the head changes continually and 
capriciously ; on the whole, while the comet is approach- 
ing the sun, the head usually contracts, expanding again 
as it recedes. 

No entirely satisfactory explanation is known for this behavior, 
but Sir John Herschel has suggested that the change is merely optical, 
. — that near the sun a part of the nebulous matter is evaporated 



MASS OF COMETS 263 

by the solar heat and so becomes invisible, condensing and reappear- 
ing again when the comet gets to cooler regions. 

The nucleus ordinarily has a diameter ranging from 
100 miles up to 5000 or 6000, or even more. Like the 
comet's head, it also varies greatly in diameter, even from 
day to day, so that it is probably not a solid body. Its 
changes, however, do not seem to depend in any regular 
way upon the comet's distance from the sun, but rather 
upon its activity in throwing off jets and envelopes. 

The tail of a comet, as regards simple magnitude, is 
by far the most imposing feature. Its length is sel- 
dom less than from 5,000000 to 10,000000 miles. It 
frequently attains 50,000000, and there are several cases 
where it has exceeded 100,000000; while its diameter, at 
the end remote from the gomet, varies from 1,000000 
to 15,000000. 

302. Mass of Comets. — While the bulk of comets is 
thus enormous, their masses are apparently insignificant, — 
in no case at all comparable with that of our little earth 
even. The evidence on this point, however, is purely neg- 
ative ; it does not enable us in any case to say just what 
the mass really is, but only to say how great it is not; 
i.e., it only proves that a comet's mass is not greater than 
tWo "oo °^ the earth's, 1 — how much less we cannot yet 
find out. The evidence is derived from the fact that no 
sensible perturbations are produced in the motions of a 
planet when a comet comes even very near it, although 
in such a case the comet itself is fairly " sent kiting," 

1 One one-hundred-thousandth of the earth's mass is about ten times 
the mass of the earth's whole atmosphere and is equivalent to the mass 
of an iron ball about 150 miles in diameter. 



264 LESSONS IN ASTRONOMY 

thus showing that gravitation has its full effect between 
the two bodies. 

Lexell's comet in 1770, and Biela's comet on several occasions, 
have come so near the earth that the computed length of the comet's 
period was changed by several weeks, while the year was not altered 
by so much as a single second. It would have been changed by 
many seconds if the comet's mass had been as much as jottooo °f 
that of the earth. 

303. Density of Comets. — This is, of course, almost 
inconceivably small, the mass of comets being so minute 
and their volume so enormous. If the head of a comet 
50,000 miles in diameter has a mass i-q-oVoo" ^ a ^ °^ ^he 
earth, its mean density must be about $-$■$■$ that of the air 
at the sea-level, — far below that of the best air-pump 
vacuum. As for the tail, the density must be almost 
infinitely lower yet. It is nearer to an " airy nothing " 
than anything else we know of. 

The extremely low density of comets is shown also by 
their transparency. Small stars can be seen through the 
head of a comet 100,000 miles in diameter, even very near 
its nucleus, and with hardly a perceptible diminution of 
their luster. 

We must bear in mind, however, that the low mean density of a 
comet does not necessarily imply a low density of its constituent 
particles. A comet may be to a considerable extent composed of 
small heavy bodies and still have a low mean density, provided they 
are far enough apart. There is much reason, as we shall see, -for 
supposing that such is really the case, — that the comet is largely 
composed of small meteoric stones, carrying with them a certain 
quantity of enveloping gas. 

Another point should be referred to. Students often 
find it impossible to conceive how such impalpable u dust 



THE LIGHT OF COMETS 265 

clouds" can move in orbits like solid masses, and with 
such enormous velocities. They forget that in a vacuum 
a feather falls as swiftly as a stone. Interplanetary space 
is a vacuum far more perfect than anything we can pro- 
duce by air-pumps, and in it the lightest bodies move as 
freely and swiftly as the densest, since there is nothing to 
resist their motion. If all the earth were suddenly anni- 
hilated except a single feather, the feather would keep right 
on and continue the same orbit with unchanged speed. 

304. The Light of Comets. — To some extent their light 
may be mere reflected sunlight, but in the main it is light 
emitted by the comet itself under the stimulus of solar 
action. That the light depends in some way on the sun 
is shown by the fact that its brightness usually varies with 
its distance from the sun, according to the same law as 
that of a planet. 

But the brightness frequently varies rapidly and capri- 
ciously without any apparent reason ; and that the comet 
is self-luminous when near the sun is proved by its spectrum, 
which is not at all like the spectrum of reflected sunlight, 
but is a spectrum of bright bands, three of which are usually 
seen and have been identified repeatedly and certainly with 
the spectrum of gaseous hydrocarbons. (All the different 
hydrocarbon gases give the same spectrum at the tempera- 
ture of a Bunsen burner.) This spectrum is absolutely iden- 
tical with that given by the blue base of a candle flame, or, 
better, by a Bunsen burner consuming ordinary coal gas. 

Occasionally a fourth band is seen in the violet, and when the comet 
approaches unusually near the sun, the bright lines of sodium and 
other metals (probably iron), sometimes appear. There are also a few 
comets with anomalous spectra in which different bands replace the 



266 



LESSONS IN ASTRONOMY 



ordinary ones, as in the case of Borrelly's comet of 1877. Holmes's 
comet in 1892 showed a purely continuous spectrum. The spectrum 
makes it almost certain that hydrocarbon gases are present in con- 
siderable quantity, and that these gases are somehow rendered lumi- 
nous ; not probably by any general heating, however, for there is no 




Fig. 69. —Head of Donati's Comet 
Bond 



reason to think that the general temperature of a comet is very high. 
Nor must we infer that the hydrocarbon gas, because it is so con- 
spicuous in the spectrum, necessarily constitutes most of the comet's 
mass ; more likely it is only a very small fraction of the whole. 



COMETARY PHENOMENA 



267 



305. Phenomena that accompany a Comet's Approach to 
the Sun. — When the comet is first discovered it is usually 
a mere round, hazy cloud of faint nebulosity, a little brighter 
near the middle. As it approaches the sun it brightens 
rapidly, and the nucleus appears. Then on the sunward 
side the nucleus begins to emit luminous jets, or else to 
throw off more or less symmetrical envelopes, which follow 
each other at intervals of 

some hours, expanding or 
growing fainter, until they 
are lost in the nebulosity of 
the head. 

Fig. 69 shows the envel- 
opes as they appeared in 
the head of Donati's comet 
of 1858. At one time 
seven of them were visible 
together ; very few comets, 
however, exhibit this phe- 
nomenon with such sym- 
metry. More frequently 
the emissions from the nucleus take the form of jets 
and streamers. 

306. Formation of Tail. — The tail appears to be formed 
of material which is first projected from the nucleus of 
the comet towards the sun and then afterwards repelled 
by the sun, as illustrated by Fig. 70. At least, this theory 
has the great advantage over all others which have been 
proposed that it not only accounts for the phenomenon 
in a general way, but admits of being worked out in detail 
and verified mathematically, by comparing the actual size 




Fig. 70. — Formation of a Comet's Tail 
by Matter expelled from the Head 



268 LESSONS IN ASTRONOMY 

and form of the planet's tail at different points in the orbit 
with that indicated by the theory ; and the accordance is 
usually satisfactory. 

As to the nature of this repulsive force there has been much specu- 
lation. For some time it has generally been believed to be electrical, 
and it is still probable that such forces play an important part. But 
the recent experimental demonstrations (1901-1902) of the repul- 
sive force of light-waves, long ago pointed out by Clerk Maxwell 
as a necessary consequence of his electro-magnetic theory of light 
(now regarded as established by the experiments of Herz), make it 
almost certain that this is the principal agent in driving off the come- 
tary particles. The two theories are, however, supplementary rather 
than contradictory. 

The repelled particles are still subject to the sun's gravi- 
tational attraction, and the effective force acting upon them 
is, therefore, the difference between the gravitational attrac- 
tion and the repulsion. This difference may or may not 
be in favor of the attraction, but in any case the sun's 
attracting force is, at least, lessened. The consequence is 
that those repelled particles, as soon as they get a little 
away from the comet, begin to move around the sun in 
hyperbolic orbits (see Sec. 439), which lie in the plane of 
the comet's orbit, or nearly so, and are perfectly amenable 
to calculation. 

In the case of a great comet the tail is usually a sort of 
curved, hollow cone, including the head of the comet at 
its smaller extremity ; in smaller comets the tail is gener- 
ally a comparatively narrow streamer where it issues from 
the head of the comet, brushing out as it recedes, and often 
showing in photographs peculiar knots and condensations, 
which are not visible with the telescope. 



FORMATION OF COMETS' TAILS 269 

The tail is curved, because the repelled particles, after 
leaving the comet's head, retain their original motion, so 
that they are arranged, not along a straight line drawn 
from the sun to the comet, but on a curve convex to the 
comet's motion, as shown in Fig. 71 ; but the stronger 
the repulsion, the less the curvature and the straighter the 
tail. There is no reason to suppose that the matter driven 
off from the comet is ever recovered by it. 




Fig. 71. — A Comet's Tail at Different Points in its Orbit near Perihelion 

307. Types of Comets' Tails. — Bredichin of Moscow 
has found that the trains of comets may be classified under 
three different types, as indicated by Fig. 72. 

First. The long, straight rays, composed of matter upon which the 
solar repulsion is from ten to fifteen times as great as the attraction 
of gravity, so that the particles leave the comet with a velocity of 
four or five miles a second, which is afterwards increased until it 
becomes enormous. The nearly straight rays, shown in Fig. 67, 
belong to this type. For plausible reasons, Bredichin supposes these 
straight rays to be composed of hydrogen. 



270 



LESSONS IX ASTRONOMY 



The second type is the ordinary curved plumelike train, like 
the principal tail of Donati's comet. In trains of this type, supposed 

to be due to hydrocarbon 
vapors, the repulsive force 
varies from 2.2 times the 
attraction of gravity for 
particles on the convex 
edge of the train to half 
that amount for those on 
the inner edge. The spec- 
trum is the same as that 
of the comet's head. 

Third. A few comets 
show tails of still a third 
type, — short, stubby 
brushes, violently curved, 
and due to matter on 
which the repulsive force 
is feeble as compared 
with gravity. These are 
assigned by Bredichin to 
metallic vapors of consid- 
erable density, with an ad- 
mixture of sodium, etc. 

308. Unexplained 
and Anomalous Phe- 
nomena. — A curious 
phenomenon, not yet 
explained, is the dark 
stripe which in a large 
comet approaching the 
sun runs down the 
center of the tail, looking very much as if it were a 
shadow of the comet's head. It is certainly not a shadow, 




Fig 



72. — Biedichin's Three Types of 
Cometary Tails 




NAT URE OF COMETS 271 

however, because it usually makes more or less of an angle 
with the sun's direction. It is well shown in Fig. 69. 
When the comet is at a greater distance from the sun 
this central stripe is usually bright, as in Fig. 73 ; and 
in the case of small comets, generally all the tail they 
show is such a narrow streamer. 

Not un frequently, moreover, comets possess anomalous tails, — 

tails directed sometimes straight towards the sun and sometimes 

at right angles to that direction. 

Then sometimes there are luminous 

sheaths, which seem to envelop the 

head of the comet and project 

towards the sun (Fig. 74), or little 

clouds of cometary matter, which 

leave the main comet, like puffs of 

, , r ,. v t -, Fig. 73. — Bright-Centered Tail of 

smoke from a bursting bomb, and _ . , * A _ . or7A 

° . Coggia s Comet, June, 1874 

travel off at an angle until they 

fade away (see Fig. 74). None of these appearances are contradic- 
tory to the theory above stated though they are not yet clearly 
included in it. 

309. The Nature of Comets. — All things considered, 
the most probable hypothesis as to the constitution of a 
comet, so far as we can judge at present, is that its head 
is a swarm of small meteoric particles, widely separated 
(say pinheads, many yards apart), each carrying with it 
an envelope of rarefied gas and vapor, in which light 
is produced either by electric discharges between the 
solid particles, or by some action due to the rays of the 
sun. As to the size of the constituent particles opinions 
differ widely. Some maintain that they are large rocks ; 
Professor Newton calls a comet a " gravel bank " ; others 
say that it is a mere " dust cloud." The unquestionable 



272 LESSONS IN ASTRONOMY 

close connection between meteors and comets (Sec. 327) 
almost compels some " meteoric hypothesis." 

310. Danger from Comets. — In all probability there is very 
little. It has been supposed that comets might do us harm in three 
ways, — either by actually striking the earth or by falling into the 
sun, and thus producing such an increase of solar heat as to burn us 
up, or, finally, by filling our atmosphere with irrespirable if not 
poisonous gases. 

As regards the possibility of a collision between a comet and the 
earth, the event is certainly possible. In fact, if the earth lasts long 
enough, it is practically sure to happen, for there are several cometary 
orbits which pass nearer to the earth's orbit than the semi-diameter 
of the comet's head. 

As to the consequence of such a collision, it is impossible to speak 
with absolute confidence for want of certain knowledge as to the 
constitution of a comet. If the solid " particles " of which the main 
portion of the comet is probably composed are no larger than pin- 
heads, the result would be only a fine meteoric shower ; if, on the 
other hand, they weigh tons, the bombardment would be a very 
serious matter. It is possible too that the mixture of the comet's 
gases with our atmosphere might be a source of danger by rendering 
the air irrespirable or explosive. 

The encounters, however, will be very rare. If we accept the 
estimate of Babinet, they will occur on the average once in about 
15,000000 years. 

If a comet actually strikes the sun, which would necessarily be a 
very rare phenomenon, it is not likely that the least injury will fol- 
low. The collision might generate about as much heat as the sun 
radiates in eight or nine hours ; but the cometary particles would 
pierce the photosphere, and their heat would be liberated mostly 
below the solar surface, simply expanding by some slight amount 
the diameter of the sun, but making no particular difference in the 
amount of its radiation for the time being. There might be, and 
very likely would be, a flash of some kind at the solar surface when 
the shower of meteors struck it, but probably nothing that the 
astronomer would not take delight in observing. 






REMARKABLE COMETS 273 

311. Remarkable Comets. — Our space does not permit 
us to give full accounts of any considerable number. We 
limit ourselves to three, which for various reasons are of 
special interest. 

Biela's comet is, or rather was, a small comet some 40,000 
miles in diameter, at times barely visible to the naked eye, 
and sometimes showing a short tail. It had a period of 
6.6 years, and was the second comet of short period 
known, having been discovered by Biela, an Austrian 
officer, in 1826 (the periodicity of Encke's comet had 
been discovered seven years earlier). Its orbit comes 
within a few thousand miles of the earth's orbit, the dis- 
tance varying somewhat, of course, on account of per- 
turbations ; but the approach is sometimes so close that 
if the comet and the earth should happen to arrive at 
the same time there would be a collision. At its return, 
in 1846, it split into two. When first seen on Novem- 
ber 28, it was one and single. On December 19 it was 
distinctly pear-shaped, and ten days later it was divided. 

The twin comets traveled along for four months at an almost 
unchanging distance of about 165,000 miles, without any apparent 
effect upon each other's motions, but both very active from the physical 
point of view, and showing remarkable variations and alternations of 
brightness entirely unexplained. In August, 1852, the twins were 
again observed, then separated by a distance of about 1,500000 
miles ; but it was impossible to tell which was which. Xeither of 
them has ever been seen again, though they must have returned 
many times, and more than once in a very favorable position. 

312. There remains, however, another remarkable chap- 
ter in the story of this comet. In 1872, on November 27, 
just as the earth was crossing the track of the lost comet, 



274 LESSONS IN ASTRONOMY 

but some millions of miles behind where the comet ought 
to be, we encountered a wonderful meteoric shower. As 
Miss Clerke expresses it, perhaps a little too positively, 
" it became evident that Biela's comet was shedding over 
us the pulverized products of its disintegration." A similar 
meteoric shower occurred again in 1885 (see also Sec. 326), 
when the earth once more crossed the track of the comet; 
and still again in 1892 and 1898, — the last very feeble. 

It is not certain whether the meteor swarms thus encountered 
were the remains of the comet itself, or whether they were other small 
bodies merely following in its path. The comet must have been several 
millions of miles ahead of the place where these meteor swarms were 
met, unless it has been set back in its orbit since 1852 by some unex- 
plained and improbable perturbations. But the comet cannot be 
found, and if it still exists and occupies the place it ought to, it must 
have somehow lost the power of shining. 

313. The Great Comet of 1882. — This is the most recent 
of the brilliant comets observed in the United States, and 
will long be remembered not only for its magnificent beauty, 
but for the great number of unusual phenomena which it 
presented. It was first seen in the southern hemisphere 
about September 3, but not in the northern until the 17th, 
the day on which it arrived at perihelion. On that day it 
was independently discovered within 2° or 3° of the sun, near 
noon, by several observers, who had not before heard of its 
existence. It was visible to the naked eye in full sunshine 
for more than a week after its perihelion passage. It then 
became a splendid object in the morning sky and continued 
to be observed for six months. 

That portion of the orbit visible from the earth coincides 
almost exactly with the orbits of four other comets, — those 



THE GREAT COMET OF 1882 275 

of 1668, 1843, 1880, and 1887, with which it forms a 
" comet-group," as already mentioned (Sec. 294). The 
perihelion distances of the comets of this group are all 
less than 750,000 miles, so that they pass within 300,000 
miles of the sun's surface, i.e., right through the corona, 
and with a velocity exceeding 300 miles a second ; and 
yet this passage through the corona does not perceptibly 
disturb their motion. 

The orbit of the comet of 1882 turns out to be a very 
elongated ellipse with a period of about 800 years. The 
period of the comet of 1880 appears to be only seventeen 
years, while the orbits of the other three are sensibly 
parabolic. 

314. Early in October the comet presented the ordinary 
features. The nucleus was round, a number of well- 
marked envelopes were visible in the head^ and the dark 
stripe down the center of the tail was sharply defined. 
Two weeks later the nucleus had been broken up and 
transformed into a crooked stream some 50,000 miles in 
length, of five or six bright points; the envelopes had 
vanished from the head, and the dark stripe was replaced 
by a bright central spine. 

At the time of perihelion the comet's spectrum was 
filled with countless bright lines. Those of sodium were 
easily recognizable, and continued visible for weeks; the 
other lines continued only a few days and were not 
certainly identified, although the general aspect of the 
spectrum indicated that iron, manganese, and calcium 
were probably present. By the middle of October it 
had become simply the normal comet spectrum with the 
ordinary hydrocarbon bands. 



276 LESSONS m ASTRONOMY 

The comet was so situated that the tail was directed 
nearly away from the earth, and so was not seen to good 
advantage, never having an apparent length exceeding 35°. 
The actual length, however, at one time was more than 
100,000000 miles. 

A unique, and still only doubtfully explained, phenom- 
enon, was a faint, straight-edged " sheath " of light, which 




Fig. 74. — The " Sheath," and the Attendants of the Comet of 1882 

enveloped the portions of the comet near the head and 
projected 3° or 4° in front of it, as shown in Fig. 74. 
Moreover, there were certain shreds of cometary matter 
accompanying the comet at a distance of 3° or 4° when 
first seen, but gradually receding and growing fainter. 



PHOTOGRAPHY OF COMETS 277 

This also was something new in cometary history, though 
the Lexell-Brooks comet, 1889- V, has since shown some- 
thing much like it. 

Holmes's comet of 1892-1893 was in many ways remarkable. 
When first discovered it was already visible to the naked eye and 
was apparently almost stationary, fast increasing in size as if swiftly 
approaching. For a time a popular impression prevailed that it was 
Biela's lost comet and might strike the earth, which led to some- 
thing like a " newspaper panic " in certain quarters. It was, how- 
ever, really receding, and never came nearer than 150,000000 miles. 
It was never conspicuous, and had no nucleus or notable train, but 
its bulk was enormous ; at one time its diameter exceeded 800,000 
miles. It experienced many capricious changes of apparent size and 
brightness, and its spectrum was purely continuous, — a thing unprec- 
edented in comets. It moves in an orbit like that of an asteroid, with 
its perihelion just outside the orbit of Mars and its aphelion close to 
that of Jupiter, its period being a few days less than seven years. 

314*. Photography of Comets. — It is now possible to 
photograph comets, and the photographs bring out numer- 
ous peculiarities and details, which are not visible to the 
eye even with telescopic aid. This is especially the case 
in the comet's tail. The figure on the next page is from 
a magnificent photograph of Rordame's comet of 1893, 
for which we are indebted to the kindness of Professor 
Holden, director of the Lick Observatory. As the camera 
was kept pointed at the head of the comet (which was mov- 
ing pretty rapidly), the star images, during the hour's 
exposure, are drawn out into parallel streaks, the little 
irregularities being due to faults of the clockwork and 
vibrations of the telescope. The knots and streamers, 
which characterize the comet's tail, were none of them 
visible in the telescope and are not the same shown upon 




Fig. 75. — Comet Rordame, July 13, 1893 
Photographed by W. J. Hussey, at the Lick Observatory 



278 



PHOTOGRAPHY OF COMETS 



279 



plates taken the day before and the day after. Other 
plates, made the same evening a few hours earlier and 
later, indicate that the " knots " were swiftly receding 
from the comet's head at a rate exceeding 150,000 
miles an hour. It is to be noted also that the light 
of a comet's 
tail seems to 
be specially 
"actinic," so 
that, as in the 
case of the 
nebulae, photo- 
graphs show 
features and 
details which 
are entirely 
invisible in 
telescopes. 

Fig. 76 shows Swift's comet of 1892, at three different 
dates as photographed by Barnard at the Lick Observa- 
tory. The rapid changes in the structure of the tail are 
very remarkable and significant. 

In 1892 Barnard discovered a small comet by the streak it left 
upon one of his star plates, and several similar discoveries have since 
been made by others. 




Fig. 76. — Swift's Comet of 1892 
Photographed by Barnard 



METEORS AND SHOOTING-STARS 

315. Meteorites. — Occasionally bodies fall upon the 
earth out of the sky. Such a body during its flight 
through the air is called a u Meteor " or " Bolide," and the 



280 LESSONS IN ASTRONOMY 

pieces which fall to the earth are called " Meteorites," 
" Aerolites," " Uranolites," or simply " meteoric stones." 
If the fall occurs at night, a ball of fire is seen, which 
moves with an apparent velocity depending upon the dis- 
tance of the meteor and the direction of its motion. The 
fire-ball is generally followed by a luminous train, which 
sometimes remains visible for many minutes after the meteor 
itself has disappeared. The motion is usually somewhat 
irregular, and here and there along its path the meteor 
throws off sparks and fragments and changes its course 
more or less abruptly. Sometimes it vanishes by simply 
fading out in the air, sometimes by bursting like a rocket. 
If the observer is near enough, the flight is accompanied 
by a heavy continuous roar, emphasized now and then by 
violent detonations. 

The observer must not expect to hear the explosion at the moment 
when he sees it, since sound travels only about twelve miles a minute. 

If the fall occurs by day, the luminous appearances are 
mainly wanting, though sometimes a white cloud is seen, 
and the train may be visible. In a few cases aerolites 
have fallen almost silently, and without warning. 

316. The Aerolites themselves. — The mass that falls is 
sometimes a single piece, but more usually there are many 
fragments, sometimes numbering thousands ; so that, as 
the old writers say, " it rains stones." The pieces observed 
to fall weigh from six hundred pounds to a few grains, 
the aggregate mass sometimes amounting to a number of 
tons. By far the greater number of aerolites are stones, but 
a few — perhaps three or four per cent of the whole num- 
ber — are masses of nearly pure iron more or less alloyed 



THE AEROLITES THEMSELVES 281 

with nickel. There are also masses of so-called " meteoric 
iron " which have been found (not seen to fall) in places 
where it is not easy otherwise to account for their pres- 
ence, and one of these (Peary's, from Greenland) weighs 
nearly seventy tons. But their meteoric character is con- 
sidered extremely doubtful by the highest authorities. 

The total number of meteorites which have fallen and been gath- 
ered into cabinets since 1800 is about 275, — only 10 of which are 
iron masses. Nearly all, however, contain a large percentage of iron, 
either in the metallic form or as sulphide. Between 25 and 30 of 
the 250 fell within the United States, the most remarkable being 
those of Weston, Conn., in 1807 ; New Concord, Ohio, 1860 ; 
Amana, Iowa, 1875; Emmet County, Iowa, 1879 (mainly iron); 
and Johnson County, Ark., 1886 (iron). 

Twenty-five of the chemical elements have been found 
in these bodies, including helium (Sec. 181), but not one 
new element ; though a large number of new minerals (i.e., 
neiv compounds of known elements) appear in them, and 
seem to be characteristic of aerolites. 

The most distinctive external feature of a meteorite is 
the thin, black, varnishlike crust that covers it. It is 
formed by the melting of the surface during the meteor's 
swift flight through the air, and in some cases penetrates 
the mass in cracks and veins. The surface is generally 
somewhat uneven, having " thumb-marks " upon it, — 
hollows, probably formed by the fusion of some of the 
softer minerals. Fig. 77 is from a photograph of a mete- 
orite weighing twenty-four pounds, which fell in Hungary 
in 1837, — one of several which fell together. 

317. Path and Motion. — When a meteor has been well 
observed from a number of different stations, its path can 



282 



LESSONS IN ASTRONOMY 



be computed. Tt usually is first seen at an altitude of 
between 80 and 100 miles and disappears at an altitude of 
between 5 and 10. The length of the path may be any- 
where from 50 to 500 miles. In the earlier part of its 
course the velocity ranges from 10 to 40 miles a second, 
but this is greatly reduced before the meteor disappears. 

In observing these bodies, the object should be to obtain as accu- 
rate an estimate as possible of the altitude and azimuth of the meteor 




Fig. 77.— The Gross Divina Meteorite 



at moments which can be identified, and also of the time occupied in 
traversing definite portions of the path. The altitude and azimuth 
will enable us to determine the height and position of the meteor, 
while the observations of the time are necessary in computing its 
velocity. By night the stars furnish the best reference points from 
which to determine its position. By day one must take advantage 
of natural objects or buildings to define the meteor's place, the 
observer marking the precise spot where he stood. By taking the 
proper instrument to the place afterwards it is then easy to ascer- 
tain the bearings and altitude. As to the time of flight, it is usual 



LIGHT AND HEAT OF METEORS 283 

for the observer to begin to repeat rapidly some familiar verse of 
doggerel when the meteor is first seen, reiterating it until the meteor 
disappears. Then, by rehearsing the same before a clock, the 
number of seconds can be pretty accurately determined. 

318. The Light and Heat of Meteors. — These are due 
simply to the destruction of the meteor's velocity by the 
friction, compression, and resistance of the air. When a 
body moving with a high velocity is stopped by the resist- 
ance of the air, the greater part of its energy is trans- 
formed into heat. Lord Kelvin has demonstrated that the 
heating effect in the case of a body moving through the 
air with a velocity exceeding ten miles a second is 
the same as if it were " immersed in a flame having a tem- 
perature at least as high as the oxyhydrogen blowpipe " ; 
and, moreover, this temperature is independent of the 
density of the air, — depending only on the velocity of the 
meteor. Where the air is dense, the total quantity of 
heat (i.e., the number of calories developed in a given time) 
is, of course, greater than where the air is rarefied ; but the 
virtual temperature of the air itself where it rubs against 
the surface is the same in either case!. During the 
meteor's flight, its surface, therefore, is raised to a white 
heat and melted, and the liquefied portions are swept off 
by the rush of air, condensing as they cool to form the 
train. In some cases this train remains visible for many 
minutes, — a fact not easily explained. It seems probable 
that the material must be phosphorescent. 

319. Origin of Meteors. — They cannot be, as some have 
maintained, the immediate product of eruptions from vol- 
canoes, either terrestrial or lunar, since they reach our 
atmosphere with a velocity which makes it certain that 



284 LESSONS IN ASTRONOMY 

they come to us from the depths of space. There is no 
proof that they have originated in any way different from 
the larger heavenly bodies. At the same time many of 
them resemble each other so closely as almost to compel 
the surmise that these, at least, must have had a common 
source. It is not perhaps impossible that such may be 
fragments which long ago were shot out from now extinct 
lunar volcanoes with a velocity which made planets of 
them for the time being. If so, they have since been 
traveling in independent orbits until they encountered 
the earth at the point where her orbit crosses theirs. Nor 
is it impossible that some of them were thrown out by 
terrestrial eruptions when the earth was young, or that 
they have been ejected from other planets, or even from 
the stars. It is only certain that during the period 
immediately preceding their arrival upon the earth they 
have been traveling in long ellipses, or parabolas, around 
the sun. 

SHOOTING-STARS 

320. Their Nature and Appearance. — These are the 
evanescent, swiftly moving, starlike points of light which 
may be seen every few minutes on any clear moonless 
night. They make no sound, nor has anything been 
certainly known to reach the earth's surface from them. 

For this reason it is probably best to retain, provisionally, at 
least, the old distinction between them and the great meteors from 
which aerolites fall. It is quite possible that the distinction has no 
real ground, that shooting-stars, as is maintained by many, are 
just like other meteors, except that being so small they are entirely 
consumed in the air ; but then, on the other hand, there are some 
things which rather favor the idea that the two classes differ in 



SHOOTING-STARS 285 

about the same way as asteroids do from comets. We know that an 
aerolitic meteor is a compact mass of rock. It is possible, and not 
even unlikely, that a shooting-star, on the contrary, is a little dust 
cloud, — like a puff of smoke. 

321. Number of Shooting-Stars. — Their number is enor- 
mous. A single observer averages from four to eight an 
hour; but if the observers are sufficiently numerous and 
so placed as to be sure of noting all that are visible from 
a given station, about eight times as many are counted. 
From this it has been estimated that the total number 
which enter our atmosphere daily must be between 
10,000000 and 20,000000, the average distance between 
them being some 200 miles. 

Besides those which are visible to the naked eye, there is a still 
larger number of meteors which are so small as to be observable 
only with the telescope. 

The average hourly number about six o'clock in the 
morning is double the hourly number in the evening, 
the reason being that in the morning we are in front 
of the earth as regards its orbital motion, while in the 
evening we are in the rear. In the evening we see only 
such as overtake us ; in the morning we see all that we 
either meet or overtake. 

322. Elevation, Path, and Velocity. — By observations 
made at stations 30 or 40 miles apart it is easy to deter- 
mine these data with some accuracy. It is found that on 
the average the shooting-stars appear at a height of about 
74 miles and disappear at an elevation of about 50 miles, 
after traversing a course 40 or 50 miles long, with a velocity 
from 10 to 50 miles a second, — about 25 on the average. 
They do not first become visible at so great a height as 



286 LESSONS IN ASTRONOMY 

the aerolitic meteors, and they are more quickly consumed 
and therefore do not penetrate the atmosphere so deeply. 

323. Brightness, Material, and Mass. — Now and then 
a shooting-star rivals Jupiter or even Venus in bright- 
ness. A considerable number are like first-magnitude 
stars, but the great majority are faint. The bright ones 
generally leave trains. Occasionally it has been possible 
to get a "snap shot," so to speak, at the spectrum of a 
meteor, and in it the bright lines of sodium and magne- 
sium (probably) are fairly conspicuous among many others 
which cannot be identified by such a hasty glance. 

Since these bodies are consumed in the air, all that we 
can hope to get of their material is their " ashes." 

In most places its collection and identification is, of course, hope- 
less ; but the Swedish naturalist Nordenskiold thought that it might 
be found in the polar snows. In Spitzbergen he therefore melted 
several tons of snow, and on filtering the water he actually detected 
in it a sediment containing minute globules of oxide and sulphide 
of iron. Similar globules have also been found in the products of 
deep-sea dredging. They may be meteoric ; but what we now know 
of the distance to which smoke and fine volcanic dust is carried 
by the wind makes it not improbable that they may be of purely 
terrestrial origin. 

We have no way of determining the exact mass of a 
shooting-star ; but from the light it emits, as seen from a 
known distance, an approximate estimate can be formed, 
since we know roughly how much energy corresponds to 
the production of a given amount of light. It is likely, 
on the whole, that an ordinary meteor and a good elec- 
tric incandescent lamp do not differ widely in what is 
called their " luminous efficiency," i.e., the percentage of 
their total energy which is converted into visible light. 



METEORIC SHOWERS 



287 



Calculations on this basis indicate that ordinary shooting- 
stars are very minute, weighing only a small fraction of an 
ounce, — from less than a grain up to fifty or one hundred 
grains for a very large one. Still this is hardly certain ; 
the estimates of some investigators would make them 
considerably larger. 

324. Meteoric Showers. — There are occasions when these 
bodies, instead of showing themselves here and there in 




Fig. 78.— The Meteoric Radiant in Leo, Nov. 13, 1867 

the sky at intervals of several minutes, appear in showers 
of thousands ; and at such times they do not move at 
random, but all their paths diverge or radiate from a single 
point in the sky, known as the radiant; i.e., their paths 
produced backwards all pass through this point, though 
they do not usually start there. Meteors which appear 



288 LESSONS IN ASTRONOMY 

near the radiant are apparently stationary, or describe 
paths which are very short, while those in the more 
distant regions of the sky pursue long courses. The 
radiant keeps its place among the stars nearly unchanged 
during the whole continuance of the shower, and the 
shower is named according to the place of the radiant. 
Thus, we have the " Leonids," or meteors whose radiant is 
the constellation of Leo, the "Andromedes" (or Bielids), 
the " Perseids," the " Lyrids," etc. 

Fig. 78 represents the tracks of a large number of the Leonids of 
1867, showing the positions of the radiant near Zeta Leonis. 

The radiant is explained as a mere effect of perspective. 
The meteors are all moving in lines nearly parallel with 
each other when encountered by the earth, and the radi- 
ant is simply the perspective " vanishing point" of this 
system of parallels. Its position depends entirely on 
the direction of the motion of the meteors with respect 
to the earth. For various reasons, however, the paths 
of the meteors, after they enter the air, are not exactly 
parallel, and in consequence the radiant is not a mathe- 
matical point, but a " spot " in the sky, often covering an 
area of 3° or 4° square. 

Probably the most remarkable of all the meteoric showers 
that ever occurred was that of the Leonids, on Nov. 12, 
1833. The number of meteors at some stations was esti- 
mated as high as 100,000 an hour for five or six hours. 
" The sky was as full of them as it ever is of snowflakes 
in a storm." 

325. Dates of Meteoric Showers. — Such meteoric showers 
are caused by the earth's encounter with a swarm of little 



DATES OF METEORIC SHOWERS 289 

meteors, and since this swarm pursues a regular orbit 
around the sun, the earth can meet it only when she is at 
the point where her orbit cuts this path. The encounter, 
therefore, must always happen on or near the same day 
of the year, except as in time the meteoric orbits shift 
their positions on account of perturbations. The Leonid 
showers, therefore, appear about November 15, and the 
Andromedes about the 27th or 28th of the same month. 

But the Leonids since 1900 have changed their date from Novem- 
ber 12 to November 15, and the Andromedes from November 27 
to November 23 since 1872, — the effect of disturbance by the 
planets. 

In some cases the meteors are distributed along their 
whole orbit, forming a sort of elliptical ring and are 
rather widely scattered. In that case the shower recurs 
every year and may continue for several weeks, as is the 
case with the Perseids, which appear in early August. 
On the other hand, the flock may be concentrated, and 
then the shower will occur only when the earth and the 
meteor swarm both arrive at the orbit-crossing together. 
This is the case with both the Leonids and the Androm- 
edes. The showers then occur, not every year, but only 
at intervals of several years, though always near the same 
day of the month. For the Leonids the interval is about 
thirty-three years, and for the Bielids about thirteen years, 
though in this case there are some intermediate showers, 
as in 1898. 

326. The meteors which belong to the same group have 
a marked family resemblance. The Perseids are yellow 
and move with medium velocity. The Leonids are very 
swift (we meet them), and they are of a bluish green tint, 



290 LESSORS m ASTKONOMY 

with vivid trains. The Bielids are sluggish (they over- 
take the earth), are reddish, being less intensely heated 
than the others, and usually have only feeble trains. 
During these showers no sound is heard, no sensible heat 
perceived, nor do any masses of matter reach the ground ; 
with one exception, however, that on Nov. 27, 1885, a 
piece of meteoric iron fell at Mazapil, in northern Mexico, 
during the shower of Andromedes, which occurred that even- 
ing. The coincidence may be accidental, but is certainly 
interesting. Some high authorities speak confidently of 
this piece of iron as a piece of BielcCs comet itself ; and 
this brings us to one of the most important astronomical 
discoveries of the last half-century. 

327. The Connection between Comets and Meteors. — At 
the time of the great meteoric shower of 1833, Professors 
Olmsted and Twining of New Haven were the first to 
recognize the " radiant" and to point out its significance 
as indicating that the meteors must be members of a swarm 
of bodies revolving around the sun in a permanent orbit. 
In 1864 Professor Newton of New Haven, taking up the 
subject anew, showed by an examination of the old records 
that there had been a number of great meteoric showers 
about the middle of November, at intervals of thirty- 
three or thirty-four years, and he predicted confidently 
the repetition of the shower on Nov. 13 or 14, 1866. It 
occurred as predicted and was observed in Europe; and 
it was followed by another in 1867, which was visible in 
America, the meteoric swarm being extended in so long a 
procession as to require more than two years to cross the 
earth's orbit. The researches of Newton and Adams 
showed that the flock was moving in a long ellipse with a 



RELATION BETWEEN COMETS AND METEORS 291 

period of thirty-three years. Another shower was pretty 
confidently expected in 1899 or 1900, but failed to appear; 
in 1901 there was, however, a well-marked, but not very 
abundant, display on the night of November 14-15. The 
failure to appear as expected is ascribed to the perturba- 
tions produced by Jupiter and Saturn since 1866. 

328. Identification of Meteoric and Cometary Orbits. — 
Within a few weeks after the shower of 1866 it was found 




Fig. 79. — Orbits of Meteoric Swarms 

that the orbit pursued by these meteors was identical with 
that of a comet, known as Tempel's, which had been visible 
about a year before ; and about the same time Schiaparelli 
showed that the Perseids, or August meteors, move in 
an orbit identical with that of the bright comet of 1862. 
Now a single coincidence might be accidental, but hardly 



QQO 



LESSONS IN ASTRONOMY 



two. Five years later came the shower of Andromedes, 
following in the track of Iliela\s comet, and among the 
more than a hundred distinct meteor swarms now rec- 
ognized Professor Alexander Ilersehel finds five others 
which are similarly related each to its special comet. It, 
is no longer possible to doubt that there is a real and 




Pig. 80. Origin <>r the Leonids 



close connection between these comets and their attendant 
meteors. Fig. 7 ( J represents four of the orbits i)( these 
cometo-meteoric bodies. 

329. Nature of the Connection. This cannot be said to 
be ascertained. In the case of the Leonids and Andro- 
medes the meteoric swarm follows the comet, but this 
does not seem to be so in the case of the IVrseids, which 
scatter along more or less abundantly every year. The 
prevailing belief IS that the comet, itself is only the thickest 



THE METEORITIC HYPOTHESIS 293 

pari of the meteoric swarm, and thai the clouds of meteors 
scattered along Its paths are the result of its disintegration ,• 
but tliis is by no means certain. 

It is easy to show that if the cornel really 18 such a swarm it must, 

at each return to perihelion gradually break up more and more, and 
disperse its constituent particles along its path until the compacl 
swarm 1ms become a diffuse ring. The longer the comet has been 
moving around the sun, the more uniformly the particles will he dis- 
tributed. The Perseids, therefore, are supposed to have been in the 
system for a Long time, while the Leonids and Andromedes are 
believed to he comparai ively new -comers. Leverrier, indeed, has gone 
so far as to indicate tin- year L26 a.i>. as the time at which Uranus 

captured Tempel's comet and brought it into the system, as illus- 
trated by Fig. so. Bu1 the theory that meteoric swarms are the 
product of cometary disintegration assumes the premise that comets 

enter the system as compact clouds, which, to say the least, is not 
yet certain. 

330. Lockyer's Meteoritic Hypothesis. Recently Sir Norman 
Lockyer has been greatly enlarging the astronomical importance of 
meteors. The probable meteoritic constitution of the zodiacal Light, 

as well as of Saturn's rings, and of the comets, has Long been 
recognized; bul he goes much farther, and maintains that all the 

heavenly bodies are either meteoric swarms, more or less condensed, 

or the final products of such condensation. Upon this hypothesis he 

attempt- to explain the evolution of the planetary system, the phe- 
nomena of variable and colored stars, the various classes of stellar 
spectra, and the forms and structure of the nebulae, indeed pretty 

much everything in the heavens from the Aurora Iiorealis to the 

sun. As a "working hypothesis," his theory Is unquestionably 
important and has at t racted much attention, hut it encounters serious 

difficulties in many of its details. 



CHAPTER XI 

THE STARS 

Their Nature, Number, and Designation — Star-Catalogues and Charts — 
Proper Motions and the Motion of the Sun in Space — Stellar Parallax — 
Star Magnitudes — Variable Stars — Stellar Spectra. 

331. The solar system is surrounded by an immense void 
peopled only by stray meteors. The nearest star, so far as 
our present knowledge goes, is one whose distance is more 
than 200,000 times as great as our distance from the sun, — 
so remote that from it the sun would look no brighter than 
the Pole-star, and no telescope yet constructed would be 
able to show a single one of all the planets. As to the 
nature of the stars, their spectra indicate that they are 
bodies resembling our sun, that is, incandescent, and 
each shining with its own peculiar light. Some are larger 
and hotter than the sun, others smaller and cooler ; some, 
perhaps large, but hardly luminous at all. They differ 
enormously among themselves, not being, as once thought, 
as much alike as individuals of the same race, but differing 
as widely as flies from elephants. 

332. Number of Stars. - - Those which are visible to the 
eye, though numerous, are by no means countless. If 
we take a limited region, the bowl of the Dipper for 
instance, we shall find that the number we can see within 
it is not very large, — hardly a dozen. In the whole 
celestial sphere the number of stars bright enough to be 

294 



THE CONSTELLATIONS 295 

distinctly seen by an average eye is only between 6000 and 
7000, even in a perfectly clear and moonless sky; a little 
haze or moonlight will cut down the number fully one-half. 
At any one time not more than 2000 or 2500 are fairly 
visible, since near the horizon the small stars (which are 
vastly the more numerous) all disappear. The total number 
which could be seen by the ancient astronomers well enough 
to be observable with their instruments is not quite 1100. 
With even the smallest telescope, however, the number 
is enormously increased. A common opera-glass brings 
out at least 100,000, and with a 2i-inch telescope Arge- 
lander made his Durchmusterung of the stars north of the 
equator, more than 300,000 in number. The Yerkes tele- 
scope, 40 inches in diameter, probably makes visible at 
least 100,000000. 

333. Constellations. — The stars are grouped in so-called 
"constellations," many of which are extremely ancient. 
All but one of those of the zodiac and most of those near 
the north pole antedate history. Their names are, for the 
most part, drawn from the Greek and Roman mythology, 
many of them being connected in some way or other with 
the Argonautic expedition. In some cases the eye, with 
the help of a lively imagination, can trace in the arrange- 
ment of the stars a vague resemblance to the object which 
gives the name to the constellation, but generally no reason 
is obvious for either name or boundaries. 

We have already, in Chap. II, given a brief description 
of those constellations which are visible in the United 
States, with maps and directions for tracing them. 

334. Designation of the Stars. — In Sec. 24 we have 
already indicated the different methods by which the 



296 LESSORS IN ASTRONOMY 

brighter stars are designated, — by proper names, position 
in the constellation, or by letters of the Greek and Roman 
alphabets. But these methods do not apply to the tele- 
scopic stars, at least to any considerable extent. Such 
stars we identify by their catalogue number, that is, we 
refer to them as number so-and-so in some star-catalogue. 
Thus, LI., 21,185 is read "Lalande, 21,185," and means 
the star so numbered in Lalande's catalogue. At present 
more than 1,000000 stars are catalogued, so that, except 
in the Milky Way, every star visible in a three-inch 
telescope can be found and identified. 

Of course all the bright stars which have names have 
letters also and are sure to be found in every catalogue 
which covers their part of the heavens. A conspicuous 
star, therefore, has usually many " aliases," and sometimes 
great care is necessary to avoid mistakes on this account. 

335. Star-catalogues are carefully arranged lists of stars, 
giving their positions (i.e., their right ascensions and declina- 
tions, or latitudes and longitudes) for a given date, usually 
also indicating their so-called magnitudes or brightness, 
and often giving still other data. The earliest of these 
star-catalogues was made about 125 B.C. by Hipparchus of 
Bithynia, the first of the world's great astronomers, and 
gives the latitudes and longitudes of 1080 stars. This 
catalogue was republished by Ptolemy 250 years later, the 
longitudes being corrected for precession; and during 
the Middle Ages several other catalogues were made by 
Arabic astronomers and those that followed them. The 
last before the invention of the telescope was that of 
Tycho Brahe, about 1580, containing 1005 stars. The 
modern catalogues are numerous ; some, like Argelander's 



STAR-CATALOGUES AJSTD CHARTS 297 

Durchmu sterling, give the places of a great number of stars 
rather roughly, merely as a means of ready identification. 
Others are "catalogues of precision," like the Pulkowa 
and Greenwich catalogues, which give the places of only 
a few hundred so-called " fundamental " stars determined 
as accurately as possible, each star by itself. Finally, we 
have the so-called " zones," which give the place of many 
thousands of stars determined accurately, but not independ- 
ently ; that is, their positions are determined bj^ reference 
to the fundamental stars in the same region of the sky. 

336. Mean and Apparent Places of the Stars. — The modern 
star-catalogue contains the mean right ascension and declination of 
its stars at the beginning of some designated year, i.e., the place the 
star would occupy if there were no nutation or aberration (Sec. 126, 
and Appendix, 435). To get the actual (apparent) right ascension 
and declination of a star for some given date, which is what we 
always want in practice, the catalogue place must be " reduced " to 
that date, i.e., it must be corrected for precession, etc. The opera- 
tion is an easy one with modern formulae and tables, but tedious 
when many stars are to be dealt with. 

337. Star Charts and Stellar Photography. — For some 
purposes accurate star charts are even more useful than 
catalogues. The old-fashioned and laborious way of mak- 
ing such charts was by "plotting" the results of zone 
observations, but at present it is being done, by means of 
photography, vastly better and more rapidly. A coopera- 
tive international campaign is now in progress, the object 
of which is to secure a photographic chart of all the stars 
down to the fourteenth magnitude. Eighteen different 
observatories have participated in the work which is now 
well advanced (1903), but its completion will probably 
require several years more. 



298 



LESSOXS IN ASTRONOMY 



One of the most remarkable things about the photo- 
graphic method is that there appears to be no limit to the 
faintness of the stars that can be photographed with a 
good instrument. By increasing the time of exposure, 

smaller and smaller stars 
are continually reached. 
With the ordinary plates 
and exposure-times not 
exceeding twenty min- 
utes, it is now possible 
to get distinct photo- 
graphs of stars that the 
eye cannot possibly see 
with the same tele- 
scope. 

Fig. 81 represents the 
photographic telescope 
(fourteen inches diame- 
ter and eleven feet focus, 
of the Paris Observa- 
tory). The other instru- 
ments engaged in the 
star-chart campaign are 
substantially like it in 
diameter and length, though differing more or less in 
mounting and in minor details. 

Until very recently the most powerful instrument of this elass was 
the Bruce photographic telescope, which has a four-lens object-glass 
of twenty-four inches diameter and eleven feet focus, taking plates 
eighteen inches square. It belongs to the observatory of Harvard 
College, but for some years has been at Arequipa, Peru. Within 




Fig. 81.- 



- Photographic Telescope of the 
Paris Observatory 



PROPER MOTION 299 

the last two or three years, however, other photographic telescopes 
of equal or greater power have been mounted at Greenwich, the 
Cape of Good Hope, Meudon, and Potsdam; the last has a photo- 
graphic object-glass of 31^ inches diameter. 

/ STAR MOTIONS 

338. The stars are ordinarily called " fixed," in distinc- 
tion from the planets, or " wanderers," because they keep 
their positions and configurations sensibly unchanged with 
respect to each other for long periods of time. Delicate 
observations, however, demonstrate that the fixity is not 
absolute, but that the star^ are really in motion. More- 
over, by the spectroscope, their rate of motion towards or 
from the earth can in some cases be approximately meas- 
ured. In fact, it appears that the velocities of the stars 
are of the same order as those of the planets : they are 
flying through space far more swiftly than cannon-balls, 
and it is only because of their enormous distance from us 
that they appear to change their positions so slowly. 

339. Proper Motion. — If we compare a star's position 
(right ascension and declination) as determined to-day with 
that observed 100 years ago, it will always be found 
to have changed considerably. The difference is due in 
the main to precession (Sec. 125) ; but after allowing for 
all such merely apparent motions of a star, it generally 
turns out that during a century the star has really altered 
its place more or less with reference to others near it, and 
this shifting of its place is called its " proper motion." Of 
two stars side by side in the same telescopic field of view 
the proper motions may be directly opposite, while, of 
course, the apparent motions will be sensibly the same. 



300 LESSONS IN ASTRONOMY 

Even the largest of these proper motions is very small. 
For many years the so-called " runaway star," 1830 Groom- 
bridge, headed the list with its annual drift of 7". But 
in 1898 it was superseded by a little star designated as 
" C. Z. (Cordova Zones), Hour V, No. 243," which has 
a proper motion of 8". 7 yearly. It would require more 
than 200 years to travel a distance equal to the moon's 
diameter. Neither of the two stars is visible to the 
naked eye. 

About a dozen stars are known to have an annual proper 
motion exceeding 3", and about 200, so far as known at 
present, exceed V 1 . The proper motions of the bright 
stars average higher than those of the faint, as might be 
expected, since, on the average, the bright ones are prob- 
ably nearer. For the first-magnitude stars, the average 
is about \ n annually, and for the sixth-magnitude stars, 
the smallest visible to the naked eye, it appears to be 
about ^y. 

Motions of this kind were first detected in 1718 by H alley, who 
found that since the time of Hipparchus the star Arcturus had 
moved towards the south nearly a whole degree, and Sirius about 
half as much. 

340. Velocity of Star Motions. — The proper motion of 
a star gives us very little knowledge as to the star's real 
motion in miles per second. The proper motion is derived 
from the comparison of star-catalogues of different dates, 
and is only the value in seconds of arc of that part of its 
motion which is perpendicular to the line of sight. A star 
moving straight towards us or from us has no proper 
motion at all, i.e., no change of apparent place which can 
be detected by comparing observations of its position. 



VELOCITY OF STAR MOTION 301 

We can, however, in some cases fix a minor limit to the 
velocity of a star. We know, for instance, that the dis- 
tance of the star, 1830 Groombridge, is certainly not less 
than 1,400000 " astronomical units," and, therefore, since 
its yearly path subtends an angle of l n at the earth, the 
length of the path must at least equal 48 astronomical 
units a year, which corresponds to a velocity of over 
140 miles a second. The real velocity must be more than 
this, but how much greater we cannot determine until we 
know how much the star's distance exceeds 140,000 units, 
and also how fast it is moving towards or from us. 

In many cases a number of stars in the same region 
of the sky have a motion practically identical, making it 
almost certain that they are real neighbors and in some 
way connected, — probably by community of origin. In 
fact, it seems to be the rule rather than the exception that 
stars which are apparently near each other are real com- 
rades ; they show, as Miss Gierke expresses it, a distinctly 
" gregarious " tendency. 

341. Radial Motion, or Motion in the Line of Sight. — 
Within the last thirty years a method l has been developed 
by which any swift motion of a star, directly towards or 
from us, may be detected by means of the spectroscope. 

If a star is approaching us, the lines of its spectrum will 
apparently be shifted towards the violet, according to 

1 It is not, as students sometimes think, by changes in the apparent 
size and brightness of a star. Theoretically, of course, a star which is 
approaching us must grow brighter ; but even the nearest star of all, 
Alpha Centauri (Sec. 343), is so far away that if it were coming directly 
towards us at the rate of 100 miles a second, it would require more than 
8000 years to make the journey ; so that in a century its brightness would 
only change about two per cent, — far too little to be noticed. 




302 LESSONS IN ASTRONOMY 

Doppler's principle (Sec. 179), and vice versa if it is 
receding from us. Visual observations of this sort, first 
made by Huggins in 1868, and since then by many others, 
succeeded in demonstrating the reality of these " radial 
motions " (in the line of sight), and in roughly measur- 
ing some of them. Later (in 1888), Vogel of Potsdam 
took up the investigation photographically, and obtained 
results that are far more satisfactory than any before 
reached. He photographs the spectrum of the star and 

the spectrum of hydrogen gas 
(or some other substance whose 
lines appear in the star spec- 
Spectrum of Rigd trum) together upon the same 

Fig. 82. -Displacement of Hy P^te, the light from both being 
Line in the Spectrum of Beta admitted through the same slit. 

If the star is not approaching or 
receding, its lines will coincide precisely with those of 
the comparison spectrum ; otherwise they will deviate one 
way or the other. 

Fig. 82 is from one of his negatives of the spectrum of Beta 
Orionis (Rigel), in which one of its dark lines is compared with the 
corresponding bright lines in the spectrum of hydrogen. The dark 
line of the stellar spectrum (bright in the negative) is shifted towards 
the red by an amount which indicates that at the time the star was 
rapidly receding. 

Still more recently the work has been taken up at several observa- 
tories in Europe and this country with instruments more powerful 
than Vogel had at his command, and with great success, especially 
by Keeler and Campbell at the Lick Observatory. Fig. 83 is enlarged 
from a recent photograph made by Frost at the Yerkes Observatory, 
showing part of the spectrum ot Alpha Persei compared with that of 
titanium; the central strip is the spectrum of the star, and it will 



THE SUN'S WAY 



303 



be seen that its dark lines are shifted towards the violet with respect 
to the bright lines of the metal, indicating that the star and earth 
were approaching each other at the rate of about 17 miles a second. 
(Only a few of the lines in the star spectrum are due to titanium, 
and not all the lines of titanium are visible in the star.) 

For the most part these radial motions of the stars, so 
far as ascertained, range between zero and sixty miles 
a second, with still higher speeds in a few exceptional 
cases. 

342. The " Sun's Way." — The proper motions of the 
stars are due partly to their own real motions, but partly 
also to the motion of the sun, which, like the other stars, 




12 3 45578 

Fig. 83. — Spectrum of Alpha Persei, compared with Titanium 
Frost, Aug. 8, 1902 

is traveling through space, taking with it its planets. Sir 
William Herschel was the first to investigate and determine 
the direction of this motion, a century ago. The principle 
involved is this: on the whole, the stars must appear to 
drift bodily in a direction opposite to the real motion of 
the solar system. 

Those in that quarter of the sky which we are approach- 
ing open out from each other, and those in the rear close 
up behind us. The motions of the individual stars lie in 
all possible directions ; but when we deal with them by 
thousands the individual is lost in the general, and the 
prevailing drift becomes obvious. 



304 LESSONS IX ASTRONOMY 

About twenty different determinations of the point 
towards which the sun's motion is directed have been 
made by various astronomers. There is a reasonable and 
almost surprising accordance of results, and they all show 
that the sun is moving towards a point in the constella- 
tion of Hercules, having a right ascension of about 267° 
(17H8 m ), and a declination of about 32° north. This 
point is called the "apex of the sun's way." As to the 
velocity of this motion of the sun, it comes out as about 
0".05 annually, seen from the average distance of a stand- 
ard sixth-magnitude star. It is assumed by high authori- 
ties, on grounds that we cannot stop to discuss, that this 
distance is about 20,000000 astronomical units, which 
would make the sun's velocity about sixteen miles a 
second, as determined from the " proper motions." 

It can, however, be more accurately deduced from the 
spectroscopic observations of radial motion. In the part 
of the heavens toward which the sun is moving the stars 
on the average seem to approach, and in the opposite 
region to recede, and the difference of the two averages is 
twice the sun's own motion, which comes out about eleven 
miles a second, — a result independent of all uncertainty 
as to the distances of the stars. 

THE PARALLAX AND DISTANCE OF STARS 

343. When we speak of the "parallax" of the sun, of 
the moon, or of a planet, we always mean the " diurnal " 
or "geocentric" parallax (Sec. 139); i.e., the apparent 
semi-diameter of the earth as seen from the body. In the 

case of a star this kind of parallax is practically nothing, 



ANNUAL OR HELIOCENTRIC PARALLAX 305 

never reaching 2 oi "oo °^ a secon( l °f arc - The expression 
"parallax of a star" always refers, on the contrary, to 
its " annual " or " heliocentric " parallax which is the appar- 
ent semi-cliameter of the earth? s orbit, as seen from the 
star. In Fig. 84 the angle at the star is its parallax. 

Even this heliocentric parallax, in the case of most 
stars, is far too small to be detected by our present 
instruments, since it never reaches a single second of arc. 
But in a few instances it has been actually measured by 
operations the most refined and difficult in the whole range 
of astronomical observation. Alpha Centauri, which is our 
nearest neighbor so far as yet known, has a parallax of 



Fig. 84. — The Annual Parallax of a Star 

about 0".9 according to the earlier observers, or only 0".75 
according to the latest authorities. There are but four or 
five other stars at present known which have a parallax 
more than half as great as this, and perhaps fifty more 
for which a sensible, but much smaller parallax has been 
detected. (For the method of determining stellar parallax, 
see Appendix, Sees. 441-443.) 

344. Unit of Stellar Distance; the Light- Year. — The 
distances of the stars are so enormous that even the radius 
of the earth's orbit, the " astronomical unit " hitherto 
employed, is far too small for convenience. It is better, 
and now usual, to take as the unit of stellar distance the 
so-called light-year, i.e., the distance which light travels 



306 LESSONS IN ASTRONOMY 

in a year. This is about 63,000 times the distance of 
the earth from the sun. 

This number is found by dividing the number of seconds in a year 
by 499, the number of seconds required by light to make the journey 
from the sun to the earth (Appendix, Sec. 432). 

A star with a parallax of 1" is at a distance of 3.26 
light-years, and in general the distance in light-years 

equals —r- 9 where p n is the parallax of the star expressed 
p' 

in seconds. 

So far as can be judged from the scanty data, it appears 
that few, if any, stars are nearer than four light-years from 
the solar system; that the naked-eye stars are probably, 
for the most part, within 200 or 300 light-years; and that 
many of the remoter stars must be thousands, or even 
tens of thousands, of light-years away. 

For the parallaxes of a number of stars, see Table V, 
Appendix. 

THE LIGHT OF THE STARS 

345. Star Magnitudes. — As has already been mentioned 
(Sec. 23), Hipparchus and Ptolemy arbitrarily divided the 
stars into six " magnitudes " according to their brightness, 
the stars of the sixth magnitude being those which are 
barely perceptible by an ordinary eye, while the first class 
comprise about twenty of the brightest. After the inven- 
tion of the telescope the same system was extended to the 
smaller stars, though without any special plan, so that 
the magnitudes assigned to telescopic stars by different 
observers are very discordant. 



THE LIGHT-RATIO OF MAGNITUDES 307 

Heis enumerates the stars clearly visible to the naked eye north 
of the 35th parallel of south declination, as follows : 

First magnitude, 14 Fourth magnitude, 313 

Second " 48 Fifth « 854 

Third « 152 Sixth " 2010 

Total, 3391 

It will be noticed how rapidly the numbers increase for the smaller 
magnitudes. Nearly the same holds good also for the telescopic stars, 
though below the tenth magnitude the rate of increase falls off. 

346, Light-Ratio and "Absolute Scale" of Star Mag- 
nitudes. — The scale of magnitudes ought to be such 
that the " light-ratio," or number of times by which the 
brightness of any star exceeds that of a star which is 
one magnitude smaller, should be the same throughout 
the whole extent of the scale. This relation was roughly, 
but not accurately, observed by the older astronomers, and 
very recently Professor Pickering of Cambridge, U.S., and 
the late Professor Pritchard of Oxford, England, have 
made photometric measurements of the brightness of 
all the naked-eye stars visible in our latitude, and have 
reclassified them according to the so-called " absolute 
scale " first proposed by Pogson about 1850, which uses 
a light-ratio equal to the fifth root of 100 (2.51 +); i.e., 
upon this scale a star of the third magnitude is 2.51 times 
brighter than one of the fourth, one of the fourth 2.51 
times as bright as one of the fifth, and so on. 

The ratio is based upon an old determination of Sir John Her- 
schel, who found that the average first-magnitude star is just about 
a hundred times as bright as a star of the sixth magnitude, five 
magnitudes fainter, so that an increase of jive in the " magnitude " 
corresponds to a hundredfold decrease of brightness. 



308 LESSONS IN ASTRONOMY 

On this scale Altair (Alpha Aquilse) and Aldebaran 
(Alpha Tauri) may be taken as standard first-magnitude 
stars, while the Pole-star and the two Pointers are very 
nearly of the standard second magnitude. 

Of course, in indicating the brightness of stars with precision, 
fractional numbers must be used, that is, we have stars of 2.4 
magnitude, etc. 

Stars that are brighter than Aldebaran or Altair have their bright- 
ness denoted by a fraction, or even by a negative number ; thus the 
absolute magnitude of Vega is 0.2, and of Sirius — 1.4. The neces- 
sity of these negative and fractional magnitudes for bright stars is 
rather unfortunate, but not really of much importance, as there are 
too few of them to cause any practical inconvenience. 

347. Magnitudes and Telescopic Power. — If a good telescope 
just shows a star of a certain magnitude, we must have a telescope 
with its aperture larger in the ratio of 1.58 : 1, in order to show stars 
one magnitude smaller (1.58 = V 2.51). A tenfold increase in the 
diameter of an object-glass theoretically carries the power of vision 
just five magnitudes lower. 

It is usually estimated that the twelfth magnitude is the limit of 
vision for a four-inch glass. It would require, therefore, a forty-inch 
glass to reach the seventeenth magnitude of the absolute scale. 

Our space does not permit any extended discussion of the photo- 
metric methods by which the brightness of stars is measured, — a 
subject which has of late attracted much attention. (See General 
Astronomy, Arts. 823-829.) 

348. Starlight compared with Sunlight. — Zollner and 
others have endeavored to determine the amount of light 1 

1 The stars send us heat also, but probably the ratio of stellar heat to 
solar does not differ much from that of starlight to sunlight. If so, the 
heat from a star is beyond the reach of any ordinary instrument. Very 
recently, however, Professor E. F. Nichols, at the Yerkes Observatory, 
with a new "radiometer," has obtained distinct and measurable heat 
effects from Arcturus and Vega. 



STARLIGHT COMPARED WITH SUXLIGHT 309 

received by us from certain stars, as compared with the 
light of the sun. According to him, Sirius gives us about 
T"oT5'Wo"o o"o "o as muc h light as the sun does, and Capella 
and Vega about -g- -$■$-$-$ V "oo" o o"o • At this rate, the standard 
first-magnitude star, like Altair, should give us about 
~, and it would take, therefore, about nine mil- 



90000000000 

lion million stars of the sixth magnitude to equal the sun. 
These numbers, however, are very uncertain. The various 
determinations for Vega vary more than fifty per cent. . 

Assuming what is only roughly true, that Argelander's magnitudes 
agree with the absolute scale, it appears that the 324,000 stars of his 
Durchmusterung, all of them north of the celestial equator, give 
a light about equivalent to 240 or 250 first-magnitude stars. How 
much light is given by stars smaller than the 9 J magnitude (which was 
his limit) is not certain. It must greatly exceed that given by the 
larger stars. As a rough guess, we may estimate that the total star- 
light of both the northern and southern hemispheres is equivalent to 
about 3000 stars like Vega, or 1500 at any one time. According to 
this, the starlight on a clear night is about ^ of the light of a full 
moon, or about 3OM000 that of sunlight. Professor Xewcomb's 
recent estimate of the total starlight is, however, only about one- 
fourth as large ; the data do not warrant any exact conclusion. 
More than ninety per cent of the light comes from stars not visible 
by the naked eye. 

349. Amount of Light emitted by Certain Stars. — When 
we know the distance of a star in astronomical units it is 
easy to compute the amount of light it really emits as com- 
pared with that given off by the sun. It is only necessary to 
multiply the light we now get from it (expressed as a fraction 
of sunlight) by the square of the star's distance in astro- 
nomical units. Thus, the distance of Sirius is about 550,000 
units, and the light we receive from it is y^^irooooo 



310 LESSONS m ASTRONOMY 

of sunlight. Multiplying this fraction by the square of 
550,000, we find that Sirius is really radiating more than 
forty times as much light as the sun. As for several other 
stars whose distance and light have been measured, some 
turn out brighter, and some darker, than the sun. The 
range of variation is very wide, and in brilliance the sun 
holds apparently about a medium rank among its kindred. 

350. Why the Stars differ in Brightness. — The appar- 
ent brightness of a star, as seen from the earth, depends 
both on its distance and on the quantity of light it emits, 
and the latter depends on the extent of its luminous sur- 
face and upon the brightness of that surface. As Bessel 
long ago suggested, " there may be as many dark stars as 
bright ones." 

Taken as a class, the bright stars undoubtedly average 
nearer to us than the fainter ones ; and just as undoubtedly 
they also average larger in diameter and more intensely 
luminous ; but when we compare any particular bright 
star with another fainter one we can seldom say to which 
of these different causes it owes its superiority. We can- 
not assert that the faint star is smaller, or darker, or 
more distant than that particular bright star, unless we 
know something more about it than the simple fact that 
it is fainter. 

351. Dimensions of the Stars. — The stars are so far 
away that their apparent diameters are altogether too small 
to be measured by any known form of micrometer. The 
sun at the distance of the nearest star would measure 1 not 
quite 0".01 across. Micrometers, therefore, do not help 

iThis does not refer, of course, to the " spurious disk" of the star 
(Appendix, Sec. 408), which is many times larger. 



VARIABLE STARS 311 

us in the matter, and until very recently we were abso- 
lutely without any positive knowledge as to the real size 
of a single one of the stars. But in 1889, by a spectro- 
scopic method more fully explained in Sec. 360, Vogel 
succeeded in showing that the bright variable star, Algol 
(Beta Persei) (Sec. 358), must have a diameter of about 
1,160000 miles, while its invisible companion is about 
840,000 miles in diameter, or just about the size of the sun. 

VARIABLE STARS 

352. Classes of Variables. — Many stars are found to 
change their brightness more or less and are known as 
" variable." They may be classed as follows : 

I. Stars which change their brightness slowly and con- 
tinuously. 

II. Those that fluctuate irregularly. 

III. Temporary stars which blaze out suddenly and then 
disappear. 

IV. Periodic stars of the type of " Omicron Ceti," usually 
having a period more or less irregular, and usually of several 
months. 

V. Periodic stars of the type of " Beta Lyrse," usually 
having periods regular and short. 

VI. Periodic stars of the " Algol " type, in which the 
period is usually short, and the variation is like what might 
be produced if the star were periodically " eclipsed " by 
some intervening object. 

353. Gradual Changes. — The number of stars which are 
certainly known to be gradually changing in brightness is 
surprisingly small. On the whole, the stars present, not 



312 LESSONS m ASTRONOMY 

only in position, but in brightness also, sensibly the same 
relations as in the catalogues of Hipparchus and Ptolemy. 

There are, however, a few instances in which it can hardly be 
doubted that considerable alteration has occurred, even within the 
last two or three centuries. Thus, in 1610, Bayer lettered Castor as 
Alpha Geminorum, while Pollux, which he called Beta Geminorum, 
is now distinctly brighter. There are about a dozen other similar 
cases known and a much larger number is suspected. 

It is commonly believed that a considerable number of stars have 
disappeared since the first catalogues were made, and that many new 
ones have come into existence. While it is unsafe to deny absolutely 
that such things may have happened, it can be said, on the other 
hand, that not a single case of the kind is certainly known. The dis- 
crepancies between the older and newer catalogues are nearly all 
accounted for by some error that has already been discovered. 

354. Irregular Fluctuations. — The most conspicuous star 
of the second class is Eta Argus (not visible in the United 
States). It varies all the way from above the first magni- 
tude (in 1843 it stood next to Sirius) down to the seventh 
magnitude (invisible to the eye). This has been its status 
ever since 1865, though some years ago it was reported as 
slightly brightening. Alpha Orionis, Alpha Herculis, and 
Alpha Cassiopeia behave in a similar way, except that their 
variation is small, never reaching an entire magnitude. 

355. Temporary Stars. — There are twelve well-authenti- 
cated instances (and a number of others more or less doubt- 
ful) of stars which have blazed up suddenly, and then 
gradually faded away. (See General Astronomy, Arts. 842- 
845.) The most remarkable of these is that known as 
Tycho's star, which appeared in the constellation of Cassi- 
opeia (Sec. 28) in November, 1572, was for some days as 
bright as Venus at her best, and then gradually faded away, 






TEMPORARY STARS 313 

until at the end of sixteen months it became invisible. 
(There were no telescopes then.) It is not certain whether 
it still exists as a telescopic star ; so far as we can judge, 
it may be any one of half a dozen which are near the place 
determined by Tycho. 

It is a notable and probably significant fact, though as yet unex- 
plained, that all these objects have appeared in or within a few 
degrees of the Milky Way. 

A temporary star, which appeared in the constellation 
Corona Borealis, in May, 1866, is interesting as having 
been the first spectroscopically examined. When near its 
brightest (second magnitude) it showed the same bright 
lines of hydrogen which are conspicuous in the solar promi- 
nences. Before its outburst it was an eighth-magnitude 
star of Argelander's catalogue, and within a few months 
it returned to its former low estate, which it still retains. 

Another instance is that of a sixth-magnitude star, which 
in August, 1885, suddenly appeared in the midst of the great 
nebula of Andromeda (Sec. 377). It showed no bright lines 
in its spectrum and in a few months it totally disappeared, 
even to the largest telescopes. 

Still more recently (in 1892) a star of the 4i magnitude 
appeared in the constellation of Auriga. At first its spec- 
trum was very complicated, showing lines both dark and 
bright, the bright lines of hydrogen and helium being espe- 
cially conspicuous. The lines were displaced by an amount 
which, according to Doppler's principle, would indicate 
radial velocities of the luminous gases amounting to more 
than 500 miles a second. It is, however, quite as likely 
that the displacements were due to intense explosive pres- 
sures (Sec. 179, last paragraph) in the luminous gases. 



;U I LESSONS IN ASTRONOMY 

In April the star became invisible, but brightened up again 
in the autumn, and then showed an entirely different spec- 
trum closely resembling that of a nebula (Sec. 880), More 
recently (in 1902) Campbell reports that its spectrum has 

become continuous, the object having apparently become 
a star again, 

355*. Nova Persei. The most recent, and one of the 
most remarkable of temporary stars, is that first seen on 
Feb. 21, 1901, when it was already as bright as the Pole- 
star. Photographs of the region made at Cambridge on 
the L9th and previous dales prove that, on the 19th it 

must still have been fainter than the twelfth magnitude. 
On the 24th it was for several hours the brightest star 
then visible, Sirins alone excepted, having increased its 
brilliance more than twenty-Jive thousand /old within live 
davs. It faded rapidly, with curious oscillations of light, 
and before the end of the year had dropped below the 
range of the eye, though still visible 4 in telescopes (January, 
L903). Its spectrum, when first photographed on Feb- 
ruary 22, was simply dark lined^ resembling that of the 
Orion stars; but by the li4l h it was transfigured and had 

become bright lined like thai of Nova Aurigee. It then 
gradually changed into the nebular type, but with the 
peculiarity that its lines were extremely broad and hazy, 

and still preserve this character, though very taint. Sev- 
eral different observers have found that its proper motion 
and parallax are insensible, its distance from US almost 

certainly exceeding a hundred light-years. 

Before the star became invisible to the eye an extensive 
nebulosity had developed around it, and in November pho- 
tographs made with the three-foot reflector of the Lick 



LIGHT CURVES OF VARIABLES 315 

Observatory, and confirmed by others from the Yerkes, 
showed that certain knots and streaks of the nebula were 
apparently moving swiftly away from the central star, — 
at a rate of several thousand miles a second (!) — unless the 
star is much nearer than the parallax observations permit 
us to assume. At present the explanation, first suggested 
by Kayser, is generally, though not universally, accepted, 
— that the motion is purely apparent, and due to a 




iPiK"imi liiifii! mi Anniml?Uimlll U 




~ r pcrl jjjjlg ; [ -mt)M- ggg j § XwWvw\ 






u 



Iffjo/ 



if mi mir 



m 



id WJi SM? 



1.1 



Fig. 85. — Light Curves of Variable Stars 

progressive illumination of denser portions of the nebula 
as the light from the great explosion travels outward 
186,000 miles a second. This would make the distance 
of the star about three hundred light-years, which is not 
at all improbable. 

356. Variables of the " Omicron Ceti" Type. — These 
objects behave almost exactly like a temporary star in 
remaining most of the time faint, rather suddenly increasing 



316 LESSONS IN ASTRONOMY 

in brightness, and then gradually fading away; but they 
do it periodically. Omicron Ceti, or Mira (i.e., "the 
wonderful ") is the type. It was discovered in 1596 and 
was the first variable star known. During most of the 
time it is of the ninth magnitude ; but at intervals of 
about eleven months it runs up to the fourth, third, or even 
second magnitude, and then back again, the whole change 
occupying about three hundred days, and the rise being 
much more rapid than the fall. It remains at its maxi- 
mum about a week or ten days. The maximum bright- 
ness varies very considerably ; and its period, while always 
about eleven months, varies to the extent of two or three 
weeks. The spectrum of the star when brightest is very 
beautiful, showing a large number of intensely bright lines, 
some of which are due to hydrogen and helium. Its light 
curve is A in Fig. 85. 1 

Nearly half of all the known variables belong to this 
class, and a large proportion of them have periods which 
do not differ very widely from a year. Most of the 
periods, however, are more or less irregular. Some writers 
include the temporary stars in this class, maintaining that 
the only difference is in the length of their period. 

357. Class V. — The variables of Class V are mostly of 
short period, and are characterized by a continual rising 
and falling of brightness, running through the whole 
period. Sometimes there are two, or even three, maxima 
before the cycle is completed. The light curve of Beta 
Lyra, the type star of this class (period about thirteen 
days), is B in Fig. 85. 

1 The light-curve diagrams are not drawn to scale, and make no pre- 
tensions to exact accuracy ; details differ for each star. 



EXPLANATION OF VARIABLES 317 

358. The " Algol' > Type. — In the stars of Class VI the 
variation is precisely the reverse of that in Class IV. The 
star remains bright for most of the time, but apparently 
suffers a periodical eclipse. The periods are mostly very 
short, ranging from ten hours to ten days. 

Algol (Beta Persei) is the type star. During most of 
the time it is of the second magnitude, and it loses about 
five-sixths of its light at the time of obscuration. The fall 
of brightness occupies about 4^ hours. The minimum 
lasts about 20 minutes, and the recovery of light takes 
about 3^ hours. The period, a little less than three days, is 
known with great precision, — to a single second indeed, — 
and is given in connection with the light curve of the star 
in Fig. 85. At present the period seems to be slowly 
shortening. About thirty variables of this class are now 
known, but new ones are continually found. 

359. Explanation of Variable Stars. — No single explana- 
tion will cover the whole ground. As to progressive changes, 
no explanation need be looked for. The wonder rather is 
that as the stars grow old such changes are not more rapid 
and notable than they are. With few exceptions there has 
been no obvious alteration since the days of Ptolemy. 

As for irregular changes, no sure account can yet be 
given. Where the range of variation is small (as it is in 
most cases) one thinks of spots upon the surface of the 
star, more or less like sun-spots ; and if we suppose these 
spots to be much more extensive and numerous than are 
the sun-spots, and also like them to have a regular period 
of frequency, and also that the star revolves upon its axis, 
we find in the combination a possible explanation of a 
large proportion of all the variable stars. 



318 LESSONS IN ASTRONOMY 

For the temporary stars we may imagine either great 
eruptions of glowing matter, like solar prominences on an 
enormous scale, or, with Sir Norman Lockyer, we may 
imagine that they, and most of the variable stars, are only 
swarms of meteors, rather compact, but not yet having 
reached the condensed condition of our own sun. Out- 
bursts of brightness are, according to him, the result of 
collisions between such swarms. Stars of the Mira type, 
according to this theory, consist of two such swarms, the 
smaller revolving around the larger in a long oval, so that 
once in every revolution it brushes through the outer por- 
tions of the larger one. But the great irregularity in the 
periods of variables belonging to this class is hard to 
reconcile with a true orbital revolution, which usually 
keeps time accurately. 

In the case of the short-period, " punctual variables," as 
Miss Clerke calls them, of Class V, the spectroscopic phe- 
nomena in many instances seem to indicate the mutual 
interaction of two or more bodies revolving around their 
common center of gravity ; this is certainly the case with 
Beta Lyrae. Others admit of simpler explanation, as due 
to the rotation of a body of irregular form or having large 
spots on its surface. 

360. Explanation of the Algol Type. — The natural and 
most probable explanation of the behavior of these stars is 
that the periodical darkening is produced by the interposi- 
tion of some opaque body between us and the star. 

This eclipse theory, first proposed by Goodricke a hun- 
dred years ago, received a striking confirmation from the 
spectroscopic work of Vogel, who, in 1889, found by the 
method indicated in Sec. 341 that about seventeen hours 



EXPLANATION OF ALGOL 319 

before the obscuration Algol is receding from us at the 
rate of nearly twenty-seven miles a second, while seven- 
teen hours after the minimum it approaches us at the same 
rate. This is just what it ought to do if it had a large 
dark companion, and the two were revolving around their 
common center of gravity in an orbit nearly edgewise to 
the earth. When the dark star is rushing forward to 
interpose itself between us and Algol, Algol itself must be 
moving backwards, and vice versa when the dark star is 
receding after the eclipse. Vogel's conclusions are that 
the distance of the dark star from Algol is about 3,250000 
miles, that their diameters are respectively about 840,000 
and 1,160000 miles, that their united mass is about two- 
thirds that of the sun, and their density about one-fifth that 
of the sun, — not much greater than that of cork. A little 
later (1892), Mr. Chandler found evidence from a slight 
alternate shortening and lengthening of the star's period of 
variation that the pair are probably moving together around 
a third (invisible) star in an orbit about as large as that 
of Uranus, accomplishing the circuit in about 130 years. 
But Tisserand suggests a different explanation. 

361. Number and Designation of Variables and their 
Range of Variation. — Mr. Chandler's catalogue of known 
variables, with its later supplements, includes 343 objects, 
besides a considerable number of suspected variables. 

About 200 of the 343 are distinctly periodic. The rest 
of them are, some irregular, some temporary, and in respect 
to many we have not yet certain knowledge whether the 
variation is or is not periodic. 

Table IV, Appendix, contains a list of the principal 
naked-eye variables visible in the United States. 



320 LESSONS IN ASTRONOMY 

Such variable stars as had not names of their own before their 
variability was discovered are at present generally indicated by the 
letters R, S, T, etc. ; i.e., R Sagittarii is the first discovered variable 
in the constellation of Sagittarius ; S Sagittarii is the second, etc. 

In a considerable number of the earlier discovered vari- 
ables the range of brightness is from two to eight magni- 
tudes, that is, the maximum brightness exceeds the minimum 
from 6 to 1000 times. In the majority, however, the range 
is much less, — only a fraction of a magnitude. 

It is worth noting that a large proportion of the vari- 
ables, especially those of Classes IV and V, are reddish in 
their color. This is not true of the Algol type. 

Since the publication of Chandler's last catalogue in 1895 there 
has been a rapid increase in the number of known variables, largely 
as the result of the examination of photographs made at Arequipa 
on different dates. The total number at present (1903) probably 
exceeds 700, and is continually growing. 

The most remarkable discovery in this line, however, is that of 
multitudes of variables in certain star clusters. The clusters known 
as Messier 3, Messier 5, and Omega Centauri are especially notable ; 
in the first, 132 variables have been detected, in the second, 85, and 
in the last, 122. The changes are so rapid as to be obvious on 
photographs taken only two hours apart. 

STAR SPECTRA 

362. As early as 1824 Fraunhofer observed the spectra 
of a number of bright stars by looking at them with a 
small telescope with a prism in front of the object-glass. 
In 1864, as soon as the spectroscope had taken its place as 
a recognized instrument of research, it was applied to the 
stars by Huggins and Secchi. The former studied very 
few spectra, but very thoroughly, with reference to the 



CLASSES OF STELLAR SPECTRA 



321 



identification of the chemical elements in certain stars. 
He found with certainty in their spectra the lines of sodium, 
magnesium, calcium, iron, and hydrogen, and more or less 
doubtfully a number of other metals. Secchi, on the 
other hand, examined a great number of spectra, less in 
detail, but with reference to a classification of the stars 
from the spectroscopic point of view. 

363. Secchi's Classes of Spectra. — He made four classes, 
as follows : 

I. Those which have a spectrum characterized by great 
intensity of 
the dark lines 
of hydrogen, 
all other lines 
being compara- 
tively feeble or 
absent. This 
class comprises 
more than half 
of all the stars, 
— nearly all 
the stars which 
are white or 
of a bluish tinge. Sirius and Vega are its types. 

II. Those which show a spectrum resembling that of the 
sun ; i.e., marked with a great number of fine dark lines. 
Capella (Alpha Aurigae) and Pollux (Beta Geminorum) 
are conspicuous examples. The stars of this class are 
also numerous. The first and second classes together 
comprise fully seven-eighths of all the stars whose spectra 
are known. 




Fig. 86. - 



- Secchi's Types of Stellar Spectra 
Keeler 



322 LESSONS IN ASTRONOMY 

Certain stars, like Procyon and Altair, seem to be intermediate 
between the first and second classes. The Line of demarcation is by 

no means sharp. 

III. Stars which show a spectrum characterized by 
dark hands, sharply defined at the upper or more refran- 
gible edge and shading out towards the rod. Most of the 

rod stars, and a large number of the variable stars, belong- 
to this class. Some of them show also bright lines in 
their spectra. 

IV. This class comprises only a few small stars, which, 
Like the preceding, show dark bands, but shading in the 
opposite direction. Usually they also show a lew bright 
linos. There are not a few anomalous stars that will not 

fall into any of these classes. 

This classification is by no means entirely satisfactory, and 
various recodifications have been proposed for it by Vogel, Lockyer, 

and others ; and Pickering, while retaining Secchi's classes, has exten- 
sively subdivided them. On the whole, however, we give it as the 

simplest, and sufficient for many purposes. 

364. Photography of Stellar Spectra. -The observation 
of these spectra by the eye is very tedious and difficult, 
and photography comes in most effectively. Iluggins in 
England and Henry Draper in this country were the 
pioneers, but until very recently the finest results in this 

line wore those obtained by Professor E. C. Pickering, of 

Cambridge, in connection with the Draper Memorial Fund. 
At present several other observers in Europe and this conn- 
try are rivaling the Harvard work in quality at least if 
not in quantity. Pickering has recurred to the old method 

of Fraunhofer, using a prism or prisms in front of the 
object-glass of his photographic telescope, thus forming a 



PHOTOGRAPHY OF STAR SPECTRA 



323 



" slitless spectroscope." The edges of the prism or prisms 
are placed east and west. If the clockwork of the instru- 
ment followed the star exactly, the spectrum formed on 
the sensitive plate would be a mere narrow streak ; but by 
allowing the clock to gain or lose slightly, the image of the 
star will move to the east or west by a very small quantity 
during the exposure, converting the streak into a band. 

The slitless spectroscope has three great advantages : (1) it saves 
all the light which comes from the star, much of which, in the usual 



Sir i us 



Procyon 



Capella 



% 



Fig. 87. — Star Spectra 
Pickering 

form of the instrument, is lost in the jaws of the slit ; (2) by taking 
advantage of the length of a large telescope, it produces a long spec- 
trum with even a single prism ; (3) and most important of all, 
it gives on the same plate and with a single exposure the spectra of all 
the many stars {sometimes more than a hundred) whose images fall upon 
the plate. 

On the other hand, the giving up of the slit precludes the usual 
methods of identifying the lines and measuring their displacements 
by actually confronting them with comparison spectra. For instance, 
it has not yet been found possible to use the slitless spectroscope for 
determining the radical velocities of stars, i.e., their absolute rates 
of approach or recession (Sec. 341). 



324 LESSONS IN ASTRONOMY 

364*. With the eleven-inch telescope formerly belong- 
ing to Dr. Draper, and a battery of four enormous prisms 
placed in front of the object-glass, spectra are obtained 
with an exposure of thirty minutes, which, before enlarge- 
ment, are fully three inches long from the F line to the 
ultra-violet extremity. They easily bear tenfold enlarge- 
ment and show many hundreds of lines in the spectra of 
the stars which belong to Secchi's second class. Fig. 87 
shows the blue and violet portion of the spectra of Sirius, 
Procyon, and Capella as thus photographed, and brings 
out clearly the gradual transition between stars of the first 
and second classes. The photographs fail to show the 
lower portion of the spectrum, i.e., the red, yellow, and 
green ; but within a few years the use of isochromatic 
plates has made it possible to deal with these colors also. 

The spectra of all the naked-eye stars in the northern 
hemisphere have already been photographed and cata- 
logued, and the work is well advanced in the southern 
hemisphere by parties sent out from Cambridge to South 
America. Many fainter stars have also been included, 
and the matter is to be followed up with the great Bruce 
telescope mentioned in Sec. 337. 

The admirable spectrograph^ work of Vogel at Potsdam 
has been already referred to in Sec. 341, and is still going 
on with greatly increased facilities since the mounting of 
the great photographic telescope already mentioned. Other 
observatories in Europe are busy along the same line, and 
in the United States the Lick and Yerkes observatories 
are specially conspicuous. 

365. Twinkling or Scintillation of the Stars. — This phenomenon 
is purely physical, and not in the least astronomical. It depends 



SCINTILLATION OF THE STARS 325 

both upon the irregularities of refraction in the air traversed by 
the light on its way to the eye (due to winds and differences of 
temperature), and also on the fact that a star is optically a lumi- 
nous point without apparent size, — a fact which, under the circum- 
stances, gives rise to the optical phexiomenon known as interference. 
Planets which have disks measurable with a micrometer do not 
sensibly twinkle. 

The scintillation is of course greatest near the horizon, and on 
a good night it practically disappears at the zenith. When the 
image of a twinkling star is examined with the spectroscope, dark 
interference bands are seen moving back and forth in its spectrum. 



CHAPTER XII 

THE STARS (Continued) 

Double and Multiple Stars and Clusters — Nebulae — Distribution of Stars 
and Constitution of the Stellar Universe — Cosmogony and the Nebular 
Hypothesis 

366. Double Stars. — The telescope shows numerous 
cases in which two stars lie so near each other that they 
can be separated only by a high magnifying power. These 
are double stars and at present more than 12,000 such 
couples are known. There is also a considerable number 
of triple stars and a few which are quadruple. Fig. 88 
represents a few of the best known objects of each class. 
The apparent distances generally range from 30" down- 
wards, very few telescopes being able to separate stars 
closer than a quarter of a second. 

In a large proportion of cases (perhaps a third of all), 
the two components are nearly equal in brightness ; but 
in many they are very unequal : in that case (never when 
they are equal), they often present contrasts of color, and 
when they do the smaller star (for some reason not known) 
always, or with very few and doubtful exceptions, has a 
tint higher in the spectrum than that of the larger, — if the 
larger is reddish or yellow, the small star will be green, 
blue, or purple. 

Gamma Andromedae and Beta Cygni are fine examples of colored 
doubles for a small telescope. 

326 



OPTICAL AND PHYSICAL DOUBLES 



327 



367. Stars optically and physically Double. — Stars may 
be double in two ways, — optically or physically. In the 
first case they are only approximately in line with each 
other as seen from the earth ; in the second case, they are 
really near each other. In the case of stars that are only 
optically double it usually happens that after some years 




Fig. 88. — Double and Multiple Stars 



we can detect their mutual independence by the fact that 
their relative motion is in a straight line and uniform, i.e., 
one of them drifts by the other in a line which is perfectly 
straight. This is a simple consequence of the combina- 
tion of their independent " proper motions." If they are 
physically connected, we find, on the contrary, that the rel- 
ative motion is in a concave curve; i.e., taking either of 



328 LESSONS IN ASTRONOMY 

them as a center, the other one appears to move around 
it in a curve. 

The doctrine of chances shows, what direct observation 
confirms, that optical pairs must be comparatively rare 
and that the great majority of double stars must be really 
physically connected, — probably by the same attraction of 
gravitation which controls the solar system. 

368. Binary Stars. — Stars thus physically connected 
are also known as ww binary " stars. They revolve in ellip- 
tical orbits around their common center of gravity in 
periods which range from 14 years to 1500 (so far as at 
present known), while the apparent length of the ovals 
ranges from 0".4 to 40". The elder Herschel, a little 
more than a century ago, first discovered this orbital 
motion of ^binaries" in trying to ascertain the parallax 
of some of the few double stars which were known at 
his time. It was then supposed that they were simply 
optical pairs, and lie expected to detect an annual dis- 
placement of one member of the pair with reference to 
the other, from which lie could infer its annual parallax 
(Sec. 343). He failed in this, but found instead a true 
orbital motion. 

The apparent orbit is always an ellipse ; but this appar- 
ent orbit is the true orbit seen more or less obliquely, so 
that the larger star is not usually in the focus of the 
relative orbit pursued by the smaller one. If we assume 
what is probable (though certainly not proved as yet), that 
the orbital motion of the pair is under the law of gravita- 
tion, we know that the larger star must be in the focus 
of the true relative orbit of the smaller, and, moreover, 
that the latter must describe around it equal areas in equal 






ORBITS OF BINARY STARS 



329 



times. By the help of these principles we can, if we have 
observations sufficiently numerous and accurate, deduce 
from the apparent oval the true orbital ellipse ; but the 
calculation is troublesome and delicate. 

369. At present the number of pairs in which this kind of 
motion has been certainly detected exceeds 200, and it is con- 
tinually increasing as our study of the double stars goes on. About 
fifty pairs have progressed so far, either having completed an entire 
revolution or a large part of one, that it is possible to determine 
their orbits with some accuracy. 

The case of Sirius is peculiar. Nearly forty years ago it had been 
found from meridian-circle observations to be moving, for no then 
assignable reason, in a 
small orbit with a period 
of about fifty years. In 
1862 Alvan G. Clark, a 
member of the famous 
C ambridgeport firm of 
telescope makers, found 
near it a minute compan- 
ion, which explains every- 
thing ; only we have to 
admit that this faint 
attendant, which does not 

give a ten-thousandth as much light as Sirius itself, has a mass 
nearly two-fifths as great. It seems to be one of Bessel's dark stars. 
Fig. 89 represents the apparent orbits of two of the best determined 
double-star systems, Gamma Virginis and Xi Ursae Majoris. 

370. Size and Form of the Orbits. — The dimensions of 
a double-star orbit can easily be obtained if we know its 
distance from us. Fortunately, a number of stars wliose 
parallaxes have been ascertained are also binary, and 
assuming the best available data, we have the results given 
in the little table which follows, — the real semi-major 




£ Ursoe Majoris 



Fig. 89. — Orbits of Binary Stars 



330 



LESSONS IN ASTRONOMY 



axis of the orbit (in astronomical units) being always equal 

a" 
to the fraction — ? in which a 11 is the angular semi-major 

axis of the real (not apparent) orbit in seconds of arc, and 
p n the parallax of the star. But it must not be forgotten 
that there is still considerable uncertainty in the data, 
especially in the parallaxes. 



Name 


Assumed 
Parallax 


Angular 
Semi-Axis 


Real 
Semi-Axis 


Period 


Mass 
= 1 


Eta Cassiopeiae . . 

Sirius 

Alpha Centauri . . 
70 Ophiuchi .... 


0";35 
0.39 
0.75 
0.15 


8".21 

8.03 

17.70 

4.54 


23.5 
20.6 
23.6 
30.3 


195 y .8 

52.2 
81.1 
88.4 


0.33 
3.24 

2.00 
3.56 



These double-star orbits are evidently comparable in 
magnitude with the larger orbits of the planetary system, 
none of those given being smaller than the orbit of Uranus 
and none much larger than that of Neptune. In form 
they are much more eccentric than planetary orbits, and 
it has been shown that this fact can be accounted for 
as a result of " tidal evolution," operating upon a pair 
of nebulous masses, formed by the separation of a parent 
nebula into two portions which revolve around their 
common center. 

371. Masses of Binary Stars. — If we assume that the 
binary stars move under the law of gravitation, then, when 
we know the semi-major axis of the orbit and the period 
of revolution, we can easily find the mass of the pair as 
compared with that of the sun, much more easily, indeed, 
than we can determine the mass of Mercury or the 
moon, strange as it may seem. It is done simply by the 



MASSES OF BINARY STARS 331 

following equation, which we give without demonstration 
(see General Astronomy, Arts. 536 and 878): 



(M+m) 



-<?)■ 



in which (M+m) is the united mass of the two stars, S is 
the mass of the sun, a is the semi-major axis of the orbit 
of the double star in astronomical units, and t its period in 
years. The final column of the preceding table gives the 
masses of the star pairs resulting from the data given in 
the table ; but the reader must bear in mind that the 
margin of error is very considerable because of the uncer- 
tainty of the orbits and parallaxes in question. A very 
slight error in the parallax makes a very great error in the 
resulting mass. 

372. Planetary Systems attending Stars. — It is a natural ques- 
tion whether some of the small companions which we see near large 
stars may not be the " Jupiter s " of their planetary systems. We can 
only say as to this that no telescope ever constructed could even come 
near to making visible a planet which bears to its primary any such 
relations of size, distance, and brightness as Jupiter bears to the sun. 
Viewed from our nearest neighbor among the stars, Jupiter would be 
a little star of about the twenty-first magnitude, not quite 5" distance 
from the sun, which itself would look like a star of the second mag- 
nitude. To render a star of the twenty-first magnitude barely visible 
(apart from all the difficulties raised by the nearness of a larger star) 
would require a telescope more than twenty feet in diameter. If any 
of the stars have planetary systems accompanying them, we shall 
never be likely to see them until our telescopes have attained a 
magnitude and power as yet undreamed of. 

373. Spectroscopic Binaries. — One of the most interest- 
ing of recent astronomical results is the detection by the 
spectroscope of many pairs of double stars so close that no 



332 LESSONS IN ASTRONOMY 

telescope can separate them. In 1889 the bright com- 
ponent of the well-known double star Mizar (Zeta Ursse 
Majoris, Fig. 88) was found by Pickering to show the dark 
lines double in the photographs of its spectrum, at regular 
intervals of about fifty-two days. The obvious explana- 
tion is that this star is composed of two, which revolve 
around their common center of gravity in an orbit which 
is turned nearly edgewise toward us. (If it was exactly 
edgewise, the star would be variable like Algol.) 

When the stars are at right angles to the line from them 
to us, one of the two will be moving towards us, while the 
other is moving in an opposite direction ; and as a con- 
sequence, the lines in their spectra will be shifted opposite 
ways, according to Doppler's principle (Sec. 179). Now 
since the two stars are so close that their spectra overlie 
each other, the result will be simply to make the lines in 
the compound spectrum look double. From the distance 
apart of the lines the relative velocity of the stars can be 
found, and from this the size of the orbit and the mass of 
the stars. Pickering inferred from his observations that 
in the case of Mizar the relative velocity of the two com- 
ponents is about 100 miles per second, the period about 
101 days, and the distance between the two stars about the 
same as the diameter of the orbit of Mars. Later observa- 
tions by Vogel, while confirming the velocity observed by 
Pickering, have shown that the period is only 20.6 days, 
— just one-fifth of Pickering's value, making the orbit 
smaller than that of Mercury. 

Mizar is thus really a triple star, the larger of the two which are seen 
with a small telescope being the one that is thus spectroscopically 
doubled. 



SPECTROSCOPIC BINARIES 333 

The lines in the spectrum of Beta Auriga exhibit the 
same peculiarity, but the doubling occurs once in four 
days, — the velocity being about 150 miles a second and 
the diameter of the orbit about 8,000000 miles, while the 
united mass of the two stars is about tw^o and a half times 
that of the sun. 

These observations of Professor Pickering's were made 
by photographing the spectrum with the slitless spectro- 
scope (Sec. 364), and are possible only where the stars 
which compose the binary are both of them reasonably 
bright. 

374. With his slit-spectroscope, Vogel (Sec. 341), as has 
already been stated (Sec. 360), has been able to detect a 
similar orbital motion in Algol, although the companion 
of the brighter star is itself invisible. A little later, in the 
case of the bright star Alpha Yirginis (Spica), he found 
a result of the same kind. At first the photographic 
observations of the spectrum of this star appeared very 
discordant. Some days they indicated that the star was 
moving totvards us quite rapidly, and then again from 
us ; but it is found that everything can be explained by 
the simple supposition that the star is double, with a small 
companion like that of Algol, not bright enough to show 
itself by its light, but heavy enough to make its partner 
swing around in an orbit about 6,000000 miles in diameter 
once in four days, — the orbit not being quite edgewise to 
the earth, so that the dark companion does not eclipse 
Spica as Algol is eclipsed by its attendant. The variable 
stars, Delta Cephei, Beta Lyrse, and one or two others 
behave in a somewhat similar manner and probably are to 
be added to the list of spectroscopic binaries. 



334 LESSONS IN ASTRONOMY 

The most remarkable spectroscopic binaries thus far detected are, 
however, two which were discovered in 1896 by spectrum photographs 
made at Arequipa. The first is Mu 1 Scorpii, in which the relative 
velocity of the components is nearly 300 miles a second. The other 
is a little star of the fifth magnitude, known as " Lacaille 3105," in 
which the relative velocity of the two stars is 385 miles a second (!), 
and since the period is 74-f hours, the mass must be about 77 times 
that of the sun. 

At present (1903) more than sixty objects of this sort are known, 
among them Capella and the Pole-star, the latter having a period of 
3 d 23 h , and an apparent relative velocity of only four miles a second. 
The catalogue of such objects is growing rapidly. 

375. Multiple Stars (see Fig. 88). — In a considerable 
number of cases we find three or more stars connected in 
one system. Zeta Cancri consists of a close pair revolving 
in a nearly circular orbit, with a period somewhat less than 
sixty years, while a third star revolves in the same direc- 
tion around them at a much greater distance and with a 
period not less than 500 years (not yet fully determined). 
Moreover, this third star is subject to a peculiar irregularity 
in its motion, which seems to indicate that it has an invisible 
companion very near the system, the system being really 
quadruple. 

In Epsilon Lyrae we have a beautiful quadruple system, 
composed of two pairs, each binary with a period of over 
200 years. Moreover, since they have a common proper 
motion, it is probable that the two pairs revolve around 
each other in a period which can be reckoned only in 
thousands of years. 

In Theta Orionis we have a remarkable object in which 
the six components are not organized in pairs, but are at 
not very unequal distances from each other. 



STAR-CLUSTERS 



335 



376. Clusters. — There are in the sky numerous groups 
of stars, containing from a hundred to many thousand 
members. A few of them are resolvable by the naked eye, 
as, for instance, the Pleiades (Fig. 90) ; some, like Praesepe 
in Cancer, break up under the power of even an opera- 
glass (Sec. 52) ; but most of them require a large telescope 
to show the separate components. To the naked eye or 
small telescopes, if 
visible at all, they 
look like faint 
clouds of shining 
haze, but in a great 
telescope they are 
among the most 
magnificent objects 
the heavens afford. 
The cluster known 
as "13 Messier," 
not far from the 
"apex of the sun's 
way," is perhaps 
the finest. 

The question at 





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Pleione 9fc 
Atlas** 


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Fig. 90. — Map of the Pleiades 



once arises whether the stars in such a cluster are compar- 
able with our own sun in magnitude and separated from 
each other by distances like that between the sun and Alpha 
Centauri, or whether they are really small (for stars) and 
closely packed ; whether the swarm is no more distant 
than the rest of the stars or far beyond them. 

Forty years ago the prevalent view was that these clusters 
were stellar universes, — galaxies, like the group of stars to 



336 LESSONS IN ASTRONOMY 

which it was supposed the sun belongs, but so incon- 
ceivably remote that they dwindled to mere shreds of cloud. 
It is now, however, quite certain that the opposite view is 
correct. The star-clusters are among our stars and form 
a part of our own stellar universe. Large and small stars 
are often so associated in the same group as to leave no 
doubt on this point, although it has not yet been possible to 
determine the actual parallax and distance of any cluster. 

NEBULAE 

377. Besides the luminous clouds which, under the tele- 
scope, break up into separate stars, there are others which 
no telescopic power resolves, and among them some which 
are brighter than many of the clusters. These irresolvable 
objects, of which about 10,000 are now catalogued, with 
probably myriads more not yet entered on the list, are 
" nebulae." Two or three of them are visible to the naked 
eye, — one, the brightest of all and the one in which the 
temporary star of 1885 appeared, is in the constellation of 
Andromeda (see Fig. 91). Another most conspicuous and 
very beautiful nebula is that in the sword of Orion. 

The larger and brighter nebulae are, for the most part, 
irregular in form, sending out sprays and streams in all 
directions and containing dark openings and " lanes." 
Some of them are of enormous volume. The great nebula 
of Orion (which includes within its boundary the mul- 
tiple star Theta Orionis) covers several square degrees, 
and photographs show that nearly the whole constellation 
is enveloped in a faint nebulosity, the wisps attaching 
themselves especially to the brighter stars. 



THE NEBULAE 



337 



The nebula of Andromeda is not quite so extensive, but 
is more regular in its form, — a long oval with dark lanes 
in it, and a bright nucleus much like a star in the center, 
as seen in a small telescope. 

The smaller nebulae are, for the most part, more or less 
nearly oval and brighter in the center. In the so-called 




Fig. 91. — Nebula in Andromeda 
Roberts 



" nebulous stars " the central nucleus is like a star shining 
through a fog. The " planetary nebulae " are about circular 
and have a nearly uniform brightness throughout, while 
the rare " annular " or " ring nebulae " are darker in the 
center. Fig. 92 is from a photograph of the finest of these 
ring nebulae, that in the constellation of Lyra. There 



338 



LESSONS IN ASTRONOMY 



are a number of nebulae which exhibit a remarkable 
spiral structure in large telescopes. There are several 
double nebulae and a few that are variable in brightness, 
though no regularity has yet been ascertained in their 
variation. Many of the most conspicuous and interest- 
ing are, how- 
ever, extremely 
irregular in 
form and struc- 
ture, as for in- 
stance, the Tri- 
fid Nebula and 
the great nebula 
of Orion (Figs. 
93 and 94). 

The great 
majority of the 
nebulae are ex- 
tremely faint, 
even in large 
telescopes, but 
the few that 
are reasonably bright are very interesting objects. 

378. Drawings and Photographs of Nebulae. — Until very 
lately the correct representation of a nebula was an extremely 
difficult task. More or less elaborate engravings exist of 
perhaps fifty of the more conspicuous of them, but pho- 
tography has now taken possession of the field. The first 
success in this line was by Henry Draper of New York, in 
1880, in photographing the nebula of Orion. Since his 
death in 1882 great progress has been made, both in Europe 




Fig. 92. — Annular Nebula in Lyra 
Keeler 




Fig. 93.— Trifid Nebula 
Keeler 




Fig. 94. — Great Nebula in Orion 
Keeler 

330 



340 



LESSONS IN ASTRONOMY 



and in this country, and at present the photographs are 
continually bringing out new and before unsuspected 
features. Fig. 91, for instance, from a photograph of the 
nebula of Andromeda, taken by Mr. Roberts of Liverpool 

in 1888, shows that 
the so-called "dark 
lanes," which hith- 
erto had been seen 
only as straight 
and wholly myste- 
rious markings, 
are really curved 
ovals, like the di- 
visions in Saturn's 
rings. The photo- 
graph brings out 
clearly a distinct 
spiral structure 
pervading the 
whole nebula, 
which as yet has 
never been made out satisfactorily by the eye with any 
telescope. This spiral structure is found more or less evi- 
dent in nearly all nebulae according to Keeler. Fig. 95, 
the so-called "whirlpool nebula" in the constellation of 
Canes Venatici, is its finest example. 




Fig. 95. — Spiral Nebula 
Keeler 






The photographs not only show new features in old nebulae, but 
they reveal numbers of new nebulae invisible to the eye with any tele- 
scope. Thus, in the Pleiades, it has been found that almost all the 
larger stars have wisps of nebulosity attached to them, as indicated 
by the dotted lines in Fig. 90, and shown fully developed in the 






CHANGES IX NEBUL2E 



341 



photograph of Fig. 96 ; and in a small territory in and near the 
constellation of Orion, Pickering, with an eight-inch telescope, found 
upon his star plates nearly as large a number of new nebulae as of 
those that were previously known within the same boundary. 

The photographs of nebulae require generally an exposure of from 
one to two hours. The images of all the brighter stars that fall upon 
the plate are, therefore, always immensely overexposed, and seriously 
injure the picture from an artistic point of view. 

The photographic brightness of a nebula, to use such an expres- 
sion, is many times greater than its brightness to the eye, owing to 
the fact that its light consists mainly in rays which belong to the 
upper or blue portion of the spectrum. It has very little red or 
yellow in it. At least, 
this is so with all the 
nebulae whose spectra are 
characterized by bright 
lines. 

379. Changes in 
Nebulae. — It cannot be 
stated with certainty that 
sensible changes have 
occurred in any of the 
nebulae since they first 
began to be observed, — 
the early instruments 
were so inferior to mod- 
ern ones that the older 
drawings cannot be 
trusted ; but some of the 
differences between the 
older and more recent 
representations make it 

extremely likely that real changes are going on. Probably after 
a reasonable interval of time photography will settle the question. 

380. Spectra of Nebulae. — One of the most important 
of the early achievements of the spectroscope was the proof 




Fig. 96. —The Pleiades 
Roberts 



342 LESSONS IN ASTRONOMY 

that the light of many nebulae, if not all, proceeds mainly 
from glowing gas of low density, and not from aggregations 
of stars. Huggins, in 1864, first made the decisive obser- 
vation by finding bright lines in their spectra. Thus far the 
spectra of all the nebulse that show lines at all appear to 
be substantially the same. Four lines are usually easily 
observed, two of which are due to hydrogen ; but the 
other two, which are brighter than the hydrogen lines, are 
not yet identified. 

Fig. 97 shows the position of the principal lines so far visually 
observed. In the brighter nebulae a number of others are also some- 
times seen and photographs show nearly one hundred in all, among 




Fig. 97. — Spectrum of the Gaseous Nebulae 

which are several of the lines of helium. Certain stars also show the 
nebular lines in their spectra, and Mr. Campbell has found one or 
two which show bright hydrogen lines extending out on each side 
of the star spectrum in such a way as to indicate an immense 
envelope of the gas surrounding the star itself. Keeler has suc- 
ceeded in measuring the motion of several of the brightest nebulae 
by the displacement of their spectrum lines, and it appears that their 
radial velocities are of the same order as those of the stars, ranging 
usually from five to twenty miles a second. 

381. Not all nebulre show the bright-line spectrum. 
Those which do (about half the whole number) are of a 
greenish tint, at once recognizable in a large telescope. 






DISTANCE AND DISTRIBUTION OF NEBULA 343 

The white nebulae, with the nebula of Andromeda, the 
brightest of all, at their head, present only a plain con- 
tinuous spectrum, unmarked by lines of any kind. This, 
however, does not necessarily indicate that the luminous 
matter is not gaseous, for a gas under pressure gives a 
continuous spectrum, like an incandescent solid or liquid. 
The telescopic evidence as to the non-stellar constitution of 
nebulae is the same for all ; no nebula resists all attempts 
at resolution (i.e., breaking up into stars) more stubbornly 
than that of Andromeda. 

As to the real constitution of those bodies we can only 
speculate. The fact that the luminous matter in them is 
mainly gaseous does not at all make it certain that they 
do not also contain dark matter, either liquid or solid. 
What proportion of it there may be we have at present 
no means of knowing. 

382. Distance and Distribution of Nebulae As to the 

distance, until very recently we could only say that like 
the star-clusters they are within the stellar universe and 
not beyond its boundaries. This is clearly shown by the 
nebulous stars, first pointed out and discussed by the 
older Herschel. We find all gradations, from a star with 
a little faint nebulosity around it, to nebulae which show 
only the faintest spot of light in the center. It is con- 
firmed also by such peculiar associations of stars and 
nebulae as we find in the Pleiades. Moreover, in certain 
curious luminous masses known as the " Nubecula," near 
the south pole, we have stars, star-clusters, and nebulae 
promiscuously intermingling. 

In 1902, however, the parallax of a nebula was for 
the first time actually measured. Newkirk, an American 



344 LESSONS IN ASTRONOMY 

graduate student of astronomy at Munich, has published 
a determination of the parallax of the central starlike 
condensation in the annular nebula of Lyra (Fig. 92), 
and finds it to be 0'M04, which corresponds to a distance 
of about thirty-two light-years. His work is based on meas- 
urements of fifteen photographs made at the Observatory 
of the University of Minnesota in 1897, 1899, and 1900. 
The result is, however, still considered doubtful by some 
high authorities. 

Taking the sky generally, the distribution of the 
nebulae is in contrast with that of the stars. The stars, 
as we shall see, crowd together near the Milky Way. 
The nebulse, on the other hand, are most numerous just 
where the stars are fewest, as if the stars had somehow 
used up the substance of which the nebulae are made. 

THE SIDEREAL HEAVENS 

383. The Galaxy, or Milky, Way. — This is a luminous 
belt of irregular width and outline which surrounds the 
heavens nearly in a great circle. It is very different in 
brightness in different parts, and is marked here and there 
by dark bars and patches which at night look like over- 
lying clouds. For about a third of its length (between 
Cygnus and Scorpio) it is divided into two roughly par- 
allel streams. The telescope shows it to be made up almost 
entirely of small stars from the eighth magnitude down; 
it contains also numerous star-clusters, but very few true 
nebulae. 

The galaxy intersects the ecliptic at two opposite points 
not far from the solstices and at an angle of nearly 60°, the 



DISTRIBUTION OF STARS IN THE HEAVENS 345 

north " galactic pole " being, according to Herschel, in the 
constellation of Coma Berenices. As Herschel remarks : 

The " galactic plane " is to the sidereal universe much what the 
plane of the ecliptic is to the solar system, — a plane of ultimate 
reference, and the ground plan of the stellar system. 

384. Distribution of Stars in the Heavens. — It is obvi- 
ous that the distribution of the stars is not even approxi- 
mately uniform. They gather everywhere into groups 
and streams; but, besides this, the examination of any 
of the great star-catalogues shows that the average num- 
ber to a square degree increases rapidly and pretty regu- 
larly from the galactic pole to the galaxy itself, where 
they are most thickly packed. This is best shown by 
the " star-gauges " of the elder Herschel, each of which 
consists merely in an enumeration of the stars visible in 
a single field of view. He made 3400 of these gauges, 
and his son followed up the work at the Cape of Good 
Hope with 2300 more in the south circumpolar regions. 
From these data it appears that near the pole of the 
galaxy the average number of stars in a single field of 
view is only about 4 ; at 45° from the galaxy, a little over 
10; while on the galactic circle itself it is 122. 

Herschel, starting from the unsound assumption that the stars are 
all of about the same size and brightness and separated by approxi- 
mately equal distances, drew from his observations numerous unten- 
able conclusions as to the form and structure of the " galactic 
cluster," to which the sun was supposed to belong, — theories for 
a time widely accepted and even yet more or less current in popular 
text-books, though in many points certainly incorrect. 

But although the apparent brightness of the stars does 
not depend entirely, or even mainly, upon their distance, 



346 LESSONS m ASTRONOMY 

it is certain that, as a class, the faint stars are really more 
remote, as well as smaller and darker than the brighter 
ones. We may, therefore, safely draw a few inferences, 
which, so far as they go, in the main agree with Herschel. 
385. Structure of the Stellar Universe. — I. The great 
majority of the stars we see are included within a space 
having roughly the form of a rather thin flat disk, like a 
watch, with a diameter eight or ten times as great as its 
thickness, our sun being not very far from its center. 

II. Within this space the naked-eye stars are dis- 
tributed with some uniformity, but not without a tend- 
ency to cluster, as shown in the Pleiades. The smaller 
stars, on the other hand, are strongly "gregarious" and 
are largely gathered into groups and streams which have 
comparatively vacant spaces between them. 

III. At right angles to the galactic plane the stars are 
scattered more evenly and thinly than in it, and we find 
on the sides of the disk the comparatively starless region 
of the nebulae. 

IV. As to the Milky Way itself, it is not certain 
whether the stars which compose it form a sort of thin, 
flat, continuous sheet, or whether they are arranged in a 
sort of ring with a comparatively empty space in the 
middle, where the sun is situated, not far from its center. 

As to the size of the disklike space which contains most of the 
stars, very little can be said positively. Its diameter is probably as 
great as 20,000 or 30,000 light-years, — how much greater it may be 
we cannot even guess, and as to the " beyond " we are still more 
ignorant. If, however, there are other stellar systems of the same 
order as our own, these systems are neither the nebulas nor the 
clusters which the telescope reveals, but are far beyond the reach 
of any instrument at present existing. 



QUESTION OF A STELLAR SYSTEM 347 

386. Do the Stars form a System? — It is probable 
(though not certain) that gravitation operates between 
the stars, as indicated by the motion of the binaries. The 
stars are certainly moving very swiftly in various direc- 
tions, and the question is whether these motions are 
governed by gravitation, and are " orbital " in the ordinary 
sense of the word. 

There has been a very persistent belief that somewhere 
there is an enormous central sun, around which the stars 
are all circulating in the same way as the planets of the 
solar system move about our own sun. This belief has 
been abundantly proved to be unfounded. It is now 
certain that there is no such great body dominating the 
stellar universe. 

387. Maedler's Hypothesis. — Another less improbable 
doctrine is that there is a general revolution of the mass 
of stars around the center of gravity of the whole, — a 
revolution nearly in the plane of the Milky Way. Some 
years ago Maedler, in his speculations, concluded (though 
without sufficient reason) that this center of gravity of the 
stellar system was not far from Alcyone, the brightest of 
the Pleiades, and, therefore, that this star was in a sense 
the " central sun " ; and the idea is frequently met with 
in popular writings. It has no satisfactory basis, how- 
ever, nor is there yet proof of any such general revolu- 
tion, though some recent investigations rather tend to 
make it probable. 

388. On the whole, the most reasonable view seems to 
be that the stars are moving much as bees do in a swarm, 
each mainly under the control of the attraction of its 
nearest neighbors, though influenced more or less, of 



348 LESSONS IN ASTRONOMY 

course, by that of the general mass. If so, the paths 
of the stars are not " orbits " in the strict sense, i.e., they 
are not paths which return into themselves. The forces 
which at any moment act upon a given star are so nearly 
balanced that its motion must be .sensibly in a straight line 
for thousands of years at a time. 

The solar system is an absolute despotism, the sun 
supreme. Among the stars, on the other hand, there is 
no central power, but the system is a pure democracy, 
in which the individuals are controlled by the influence 
of their neighbors, and by the authority of the whole 
community to which they themselves belong. 

COSMOGONY 

389. One of the most interesting topics of speculation 
relates to the process by which the present state of things 
has come about. In a forest, to use an old comparison of 
Herschel's, we see around us trees in all stages of their 
life-history, from the sprouting seedlings to the prostrate 
and decaying trunks of the dead. Is the analogy appli- 
cable to the heavens, and can we hope by a study of the 
present condition and behavior of the bodies around us to 
come to an understanding of their past history and prob- 
able future ? Possibly to some extent. But human life is 
so short that the processes of change are hardly perceptible, 
and our telescopes and spectroscopes reveal but little of 
the "true inwardness" of things, so that speculation is 
continually baffled and its results can seldom be accepted 
as secure. Still, some general conclusions seem to have 
been reached which are likely to be true ; but the pupil 



GENESIS OF THE PLANETARY SYSTEM 349 

is warned that they are not to be regarded as established in 
any such sense as the law of gravitation and the theory 
of planetary motion. 

In a general way we may say that the gathering of 
clouds of rarefied matter or meteoritic swarms into more 
compact masses under the force of gravitation, the produc- 
tion of heat by this shrinkage, the effect of this heat upon 
the mass itself and upon neighboring bodies, — these prin- 
ciples cover nearly all the explanations that can thus far 
be given for the present condition of the heavenly bodies. 

390. Genesis of the Planetary System. — Our planetary 
system is clearly no accidental aggregation of bodies. 
Masses of matter coming haphazard to the sun would 
move (as comets actually do move) in orbits which, though 
necessarily conic sections, would have every degree of 
inclination and eccentricity. In the planetary system 
this is not so. Numerous relations exist for which gravi- 
tation does not at all account, and for which the mind 
demands an explanation. 

We note the following as the principal: 

1. The orbits of the planets are all nearly circular (i.e., never very 
eccentric, asteroids excepted). 

2. They are all nearly in one plane (excepting those of some 
of the asteroids). 

3. The revolution of all, without exception, is in the same 
direction. 

4. There is a curious and regular progression of distances (expressed 
by Bode's law, which, however, breaks down with Neptune). 

As regards the planets themselves : 

5. The plane of every planet's rotation nearly coincides with that 
of its orbit (probably excepting Uranus). 



350 LESSONS IN ASTRONOMY 

6. The direction of rotation is the same as that of the orbital 
revolution (excepting probably Uranus and Neptune). 

7. The plane of orbital revolution of the planet's satellites coin- 
cides nearly with that of the planet's rotation, wherever this has 
been ascertained. 

8. The direction of the satellites' revolution also coincides with 
that of the planet's revolution (with the same limitation). 

9. The largest planets rotate most swiftly. 

391. Now this arrangement is certainly an admirable one 
for a planetary system, and therefore some have argued that 
the Deity constructed the system in that way, perfect from 
the first. But to one who considers the way in which 
other perfect works usually attain their perfection — their 
processes of growth and development — this explanation 
seems improbable. It appears far more likely that the 
planetary system was formed by growth than that it was 
built outright. 

The theory which in its main features is now generally 
accepted, as supplying an intelligible explanation of the 
facts, is that known as the " nebular hypothesis." In a 
more or less crude and unscientific form it was first sug- 
gested by Swedenborg and Kant, and afterwards, about 
the beginning of the present century, was worked out in 
mechanical detail by Laplace. 

It was formulated before the discovery of the great 
principles of the " conservation of energy," and the equiva- 
lence of heat to other forms of energy, so that in some 
respects it is defective and doubtless wrong. The main 
idea, however, that our system was once an incoherent 
mass and has come to its present state by physical pro- 
cesses, is almost certainly correct, and forms the foundation 
of all current speculation upon the subject. 



THE NEBULAR HYPOTHESIS 351 

392. Laplace's Nebular Hypothesis. — He maintained or 
rather suggested: 

(a) That at some time in the past 1 the matter which is 
now gathered into the sun and planets was in the form of 
a " nebula." 

(b) This nebula, according to him, was a cloud of 
intensely heated gas (questionable). 

(c) Under the action of its own gravitation the nebula 
assumed a form approximately globular, with a motion of 
rotation, the whirling motion depending upon the acci- 
dental differences in the original velocities and densities 
of the different parts of the nebula. As the contraction 
proceeded the swiftness of the rotation would necessarily 
increase for mechanical reasons. 

(d) In consequence of its whirling motion the globe 
would necessarily become flattened at the poles and 
ultimately, as the contraction went on, the centrifugal 
force at the equator would there become equal to gravity 
and rings of nebulous matter would be detached from the 
central mass, like the rings of Saturn. In fact, Saturn's 
rings suggested this feature of the theory. 

(e) The ring thus formed would for a time revolve 
as a whole, but would ultimately break, and the material 
would collect into a globe revolving around the central nebula 
as a planet. 

1 As to the origin of the nebula itself he did not speculate. There was 
no assumption on his part, as is often supposed, that the matter was first 
created in the nebulous condition. He assumed only that, as the egg may 
be taken as the starting-point in the life-history of an animal, so the 
nebula is to be regarded as the starting-point of the life-history of the 
planetary system. He did not raise the question whether the egg is, or 
is not, older than the hen. 



352 LESSONS IN ASTRONOMY 

Laplace supposed that the ring would revolve as if it 
were solid, the particles at the outer edge moving more 
swiftly than those at the inner (questionable). If this 
were always so, the planet formed would necessarily rotate 
in the same direction in which the ring had revolved. 

(/) The planet thus formed would throw off rings of its 
own and so form for itself a system of satellites. 

393. This theory obviously explains most of the facts 
of the solar system, which were enumerated in the preced- 
ing article, though some of the exceptional facts (such as 
the short periods of the satellites of Mars and the retro- 
grade motions of those of Uranus and Neptune) cannot be 
explained by it alone in its original form. But even these 
exceptions do not contradict it, as is sometimes supposed. 

As to the modifications required by the theory, while 
they alter the mechanism of the development in some 
respects, they do not touch the main results. It is rather 
more likely, for instance, that the original nebula was a 
cloud of ice-cold dust than incandescent gas and "fire 
mist," to use a favorite expression; and it is likely, as 
suggested by the spiral nebulse, that planets and satellites 
were often separated from the mother orb otherwise than 
in the form of rings. 

Nor is it possible that a thin wide ring could revolve in 
the same way as a solid mass ; the particles near the inner 
edge must make their revolution in periods much shorter 
than those upon the circumference, or the ring would tear 
to pieces. But this very fact makes it possible to account 
for the peculiar backward motion of the satellites of 
Uranus and Neptune, thus removing one of the main 
objections to the theory in its original form. 



THE METEORITIC HYPOTHESIS 353 

Many things also make it questionable whether the 
outer planets are so much older than the inner ones, as 
Laplace's theory would indicate. It is not impossible that 
they may even be younger. 

Our limits do not permit us to enter into a discussion of Darwin's 
" tidal theory " of satellite formation, which may be regarded as, in 
a sense, supplementary to the nebular hypothesis ; nor can we more 
than mention Faye's proposed modification of it. According to him, 
the inner planets are the oldest. 

394. Lockyer's Meteoritic Hypothesis. — Sir Norman 
Lockyer has of late vigorously revived a theory which had 
been from time to time suggested before, viz., that all the 
heavenly bodies in their present state are mere clouds of 
meteors, or have been formed by the condensation of such 
clouds ; and it is an interesting fact, as Professor G. H. 
Darwin has recently shown, that a large swarm of meteors 
in which the individuals move swiftly in all directions 
would, in the long run and as a whole, behave almost 
exactly, from a mechanical point of view, in the same way 
as one of Laplace's hypothetical gaseous nebulse. 1 

The spectroscopic observations upon which Sir Norman rests his 
attempted demonstration are many of them very doubtful ; but that 
does not really discredit the main idea, except so far as the question 
of the origin and nature of the light of the heavenly bodies is 

1 This is not very strange, after all. According to the modern u kinetic 
theory of gases" (Rolfe's "Physics," page 157), a meteor cloud is 
mechanically just the same thing as a mass of gas magnified. The 
kinetic theory asserts that gas is only a swarm of minute molecules, the 
peculiar gaseous properties depending upon the collisions of these mole- 
cules with each other and with the walls of the inclosing vessel. Mag- 
nify sufficiently the molecules and the distances between them, and you 
have a meteoric cloud. 



354 LESSONS IN ASTRONOMY 

concerned. He makes the light depend upon the collisions between 
the meteors, and finds in the spectra of the heavenly bodies evidence 
of the presence of materials with which we are familiar in the mete- 
orites which fall upon the earth's surface. These identifications are 
in many cases questionable, — in some certainly incorrect, — and it 
seems much more likely that the luminosity depends to a great degree 
upon other than mere mechanical actions, — electrical and chemical 
for instance. 

395. Stars, Star-Clusters, and Nebulae. — It is obvious 
that the nebular hypothesis in all its forms applies to the 
explanation of the relations of these different classes of 
bodies to each other. In fact, Herschel, appealing only to 
the "law of continuity," had concluded, before Laplace 
published his theory, that the nebulae develop sometimes 
into clusters, sometimes into double or multiple stars, and 
sometimes into single stars. He showed the existence in 
the sky of all the intermediate forms between the nebula 
and the finished star. For a time, about the middle of the 
last century, while it was generally believed that all the 
nebulae were only star-clusters, too remote to be resolved 
by existing telescopes, his views fell rather into abeyance ; 
but they regained acceptance in their essential features 
when the spectroscope demonstrated the substantial differ- 
ence between gaseous nebulae and the star-clusters. 

396. Conclusions from the Theory of Heat. — Kant and 
Laplace, as Newcomb says, seem to have reached their 
results by reasoning forwards. Modern science comes to 
very similar conclusions by working backwards from the 
present state of things. 

Many circumstances go to show that the earth was once 
much hotter than it now is. As we penetrate below the 
surface, the temperature rises nearly a degree (Fahrenheit) 






CONCLUSIONS FROM THE THEORY OF HEAT 355 

for every sixty feet, indicating a white heat at the depth 
of a few miles ; the earth at present, as Lord Kelvin says, 
" is in the condition of a stone that has been in the lire and 
has cooled at the surface." 

The moon bears apparently on its surface the marks of 
the most intense igneous action, but seems now to be 
entirely chilled. 

The planets, so far as we can make out with the tele- 
scope, exhibit nothing at variance with the view that 
they were once intensely heated, while many things go 
to establish it. Jupiter and Saturn, Uranus and Neptune, 
do not seem yet to have cooled off to anything like the 
earth's condition. 

As to the sun, we have in it a body continuously pour- 
ing forth an absolutely inconceivable quantity of heat with- 
out any visible source of supply. As has been explained 
already (Sec. 192), the only rational explanation of the 
facts thus far presented is that which makes it a huge, 
cloud-mantled ball of elastic substance slowly shrinking 
under its own central gravity, and thus generating heat. 1 
A shrinkage of about three hundred feet a year in the 
sun's diameter will account for the whole annual output 
of radiant heat and light. 

397. Age of the System. — Looking backward, then, and 
trying to imagine the course of time and of events reversed, 
we see the sun growing larger and larger, until at last it 
has expanded to a huge globe that fills the largest orbit of 

1 So far we have no decisive evidence whether the sun has passed its 
maximum of temperature or not. Lockyer thinks its spectrum (resem- 
bling as it does that of Capella and the stars of the second class) proves 
that it is now on the downward grade and growing cooler ; but others do 
not consider the evidence conclusive. 



356 LESSONS IN ASTRONOMY 

our system. How long ago this may have been we can- 
not state with certainty. If we could assume that the 
amount of heat yearly radiated by the solar surface had 
remained constantly the same through all those ages, and, 
moreover, that all the radiated heat came solely from the 
slow contraction of the sun's mass, apart from any con- 
siderable original capital in the form of a high initial 
temperature, and without any reenforcement of energy 
from outside sources, — if we could assume these prem- 
ises, it is easy to show that the sun's past history must 
cover about 15,000000 or 20,000000 years. But such 
assumptions are at least doubtful ; and if we discard 
them, all that can be said is that the sun's age must be 
greater, and probably many times greater, than the limit 
we have named. 

398. Future Duration of the System. — Looking forward, 
on the other hand, from the present towards the future, it 
is easy to conclude with certainty that if the sun continues 
its present rate of radiation and contraction and receives 
no subsidies of energy from without, it must within 
5,000000 or 10,000000 years become so dense that its 
constitution will be radically changed. Its temperature 
will fall, and its function as a sun will end. Life on the 
earth, as we know life, will be no longer possible when the 
sun has become a dark, rigid, frozen globe. At least this 
is the inevitable consequence of what now seems to be the 
true account of the sun's condition and activity if nothing 
interferes with its steady and inexorable course. 

But there may be interference : catastrophes and par- 
oxysms, sudden changes and reversals of the regular course 
of events at critical moments, collisions and explosions, 



THE SYSTEM NOT ETERNAL 357 

are certainly possible and actually occur, as the phenom- 
ena of the solar surface and temporary stars abundantly 
make evident. 

399. The System not Eternal. — One conclusion seems 
to be clear : that the present system of stars and worlds is 
not an eternal one. We have before us everywhere evi- 
dence of continuous, irreversible progress from a definite 
beginning towards a definite end. Scattered particles and 
masses are gathering together and condensing, so that the 
great grow continually larger by capturing and absorbing 
the smaller. At the same time the hot bodies are losing 
their heat and distributing it to the colder ones, so that 
there is an unremitting tendency towards a uniform, and 
therefore useless, temperature throughout our whole uni- 
verse ; for heat is available as energy (i.e., it can do work) 
only when it can pass from a warmer body to a colder 
one. The continual warming up of cooler bodies at the 
expense of hotter ones always means a loss, therefore, 
not of energy, for that is indestructible, but of available 
energy. To use the ordinary technical term, energy is 
continually dissipated by the processes which constitute 
and maintain life on the universe. This dissipation of 
energy can have but one ultimate result, that of absolute 
stagnation when the temperature has become everywhere 
the same. 

If we carry our imagination backwards, we reach "a 
beginning of things," which has no intelligible antecedent; 
if forwards, we come to an end of things in dead stagnation. 
That in some way this end of things will result in a " new 
heavens and a new earth" is, of course, probable, but 
science as yet can present no explanation of the method. 



APPENDIX 



ASTRONOMICAL INSTRUMENTS 

The Celestial Globe — The Telescope: Simple, Achromatic, and Reflecting 
— The Equatorial — The Filar Micrometer — The Transit-Instrument — 
The Clock and Chronograph — The Meridian Circle — The Sextant 

400. The Celestial Globe. — The celestial globe is a ball, 
usually of papier-mache, upon which are drawn the circles of 
the celestial sphere and a map of the stars. It is ordinarily 
mounted in a framework which represents the horizon and 
the meridian in the manner shown in Fig. 98. 

The " horizon," HW in the figure, is usually a wooden ring 
three or four inches wide and perhaps three-quarters of an 
inch thick, directly supported by the pedestal. It carries 
upon its upper surface at the inner edge a circle marked with 
degrees for measuring the azimuth of any heavenly body, 
and outside this the so-called zodiacal circles, which give 
the sun's longitude and the equation of time for every day 
of the year. 

The meridian ring, MM 1 , is a circular ring of metal which 
carries the bearings upon which the globe revolves. Things 
are so arranged, or ought to be, that the mathematical axis 
of the globe is exactly in the same plane as the graduated face 
of the ring, which is divided into degrees. The meridian ring 
is held underneath the globe by a support, with a clamp which 
enables us to fix it securely in any desired position. 

The surface of the globe is marked first with the celestial 
equator, next with the ecliptic crossing the equator at an 

359 



360 



APPENDIX 



angle of 23^° at X (as the figure is drawn, not the vernal), and 
each of these circles is divided into degrees. The equinoctial 
and solstitial colures X and PE are also always represented, 
E being the pole of the ecliptic. As to the other circles, 
usage differs. The ordinary way at present is to mark the 
globe with twenty-four hour-circles 15° apart (the colures, 
Sec. 117, being four of them), and with parallels of declina- 
tion 10° apart. On the surface of the globe are plotted the 

positions of the stars 
^— - and the outlines of 

the constellations. 

It is perhaps worth 
noting that many of the 
spirited figures of the 
constellations upon our 
present globes are copied 
from designs drawn by 
Albert Dtirer for a star- 
map published in his 
time. 

The Hour-Index is 
usually a small circle 
of thin metal, about 
four inches in diam- 
eter, which is fitted 
to the northern 
pole of the globe 
with a stifiish friction, so that it can be set like the hands 
of a clock, and when once set will turn with the globe 
without shifting. 

On some globes a hand like a clock-hand is used, showing the hour 
on a circle engraved on the surface of the globe itself. This is the 
case with the globe shown in the figure. 







Fig. 98. — The Celestial Globe 



THE CELESTIAL GLOBE 361 

401. To " rectify " a Globe, — i.e., to set it so as to show 
the aspect of the heavens at any time : 

1. Elevate the north pole P of the globe to an angle equal 
to the observer's north latitude by means of the graduation on 
the meridian ring, and clamp the ring securely. 

If the observer is south of the equator, the south pole, of course, 
must be elevated instead of the north. 

2. Look up the day of the month on the horizon of the 
globe, and opposite to the day find on the zodiacal circle the 
sun's longitude for that day. 

3. On the ecliptic (upon the surface of the globe) find 
the degree of longitude thus indicated, and bring it to the 
graduated face of the meridian ring. The globe is thus set 
to correspond to apparent noon of the day in question. 

It may be well to mark the place of the sun temporarily with a bit 
of paper gummed on at the proper place in the ecliptic. It can easily 
be wiped off after using. 

4. Hold the globe fast so as to keep the place of the sun 
exactly on the meridian, and turn the hour-index until it shows 
the mean time of apparent noon (i.e., 12 h ± the equation of 
time given on the wooden horizon for the day in question). 

If standard time is used, the hour -index must be set to the standard 
time for apparent noon instead of the local mean time. 

5. Finally, turn the globe upon its axis until the hour- 
index shows the hour for which it is to be set. The globe 
will then represent the true aspect of the heavens at that time. 

The hour-index ought to keep its position unchanged while the 
globe is revolved, but the observer must watch to see that it does 
not shift ; many globes are faulty in this respect. 

The positions of the moon and planets are not given by this opera- 
tion, since they have no fixed places in the sky and therefore cannot 



362 APPENDIX 

be put in by the globe maker. If one wants them represented, he 
must look up their right ascensions and declinations in some almanac 
and mark the proper places on the globe with bits of wax or paper. 

TELESCOPES 

402. Telescopes are of two kinds, — refracting and reflecting. 
The refractor was first invented early in the seventeenth 

century and is much more used, but the largest instruments 
ever made are reflectors. In both, the fundamental principle 
is the same. The large lens of the instrument (or else its 
concave mirror) forms a real image of the object looked at, 
and this image is then examined and magnified by the eye- 
piece, which in principle is only a magnifying-glass. 

In the form of instrument, however, which was originally devised 
by Galileo and is still used as the " opera-glass," the rays from the 
object-glass are intercepted and brought to parallelism by a concave 
lens which serves as an eye-glass, before they form the image. Tele- 
scopes of this construction are never made of much power, being 
inconvenient on account of the smallness of the field of view. 

403. The Simple Refracting Telescope. — This consists 
essentially, as shown in Fig. 99, of two convex lenses : one, 
the object-glass A, of large size and long focus ; the other, the 
eye-glass B, of short focus, — the two being set at a distance 
nearly equal to the sum of their focal lengths. Kecalling the 
optical principles relating to the formation of images by lenses, 
we see that if the instrument is pointed towards the moon, for 
instance, all the rays that strike the object-glass from the top 
of the crescent will be collected to a focus at a, while those 
from the bottom, will come to a focus at b ; and correspondingly 
with rays from the other points on the surface of the moon. 
We shall, therefore, get in the " focal plane " of the object- 
glass a small inverted " image " of the moon. The image is 
a real one, i.e., the rays really meet at the focal points, so that 



TELESCOPES 363 

if we insert a photographic plate in the focal plane at ab and 
properly expose it, we shall get a picture of the object. The 
size of the picture will depend upon the apparent angular 
diameter of the object and the distance from the object-glass 
to the image ab. 

If the focal length of the lens A is ten feet, then the image of 
the moon (31' in apparent diameter) will be a little more than one 
inch in linear diameter. 

404. Magnifying Power. — If we use the naked eye we 
cannot see the image distinctly from a distance much less 
than a foot, but if we use a magnifying-lens of, say, one inch 
focus, we can view it from a distance of only an inch and 
it will look correspondingly larger. Without stopping to 




Fig. 99. — The Simple Refracting Telescope 

prove the principle, we may say that the magnifying power 
is simply equal to the quotient obtained by dividing the focal 
length of the object-glass by that of the eye-lens. 

It is to be noted, however, that a magnifying power of unity is 
sometimes spoken of as "no magnifying power at all," since the 
image appears of the same size as the object. 

The magnifying power of a telescope is changed at pleasure by 
simply interchanging the eyepieces, of w^hich every telescope of any 
pretensions always has a considerable stock giving various powers. 
These usually contain two or more lenses in order to give good 
definition over a larger field than can be obtained with a single-lens 
eyepiece. (See Sec. 409.) 

405. Brightness of the Image. — This depends not upon 
the focal length of the object-glass, but upon its diameter, or, 



364 APPENDIX 

more strictly, its area. If we estimate the diameter of the 
pupil of the eye at one-fifth of an inch, as it is usually reck- 
oned, then (neglecting the loss from want of perfect transpar- 
ency in the lenses) a telescope one inch in diameter collects 
into the image of a star 25 times as much light as the naked 
eye receives ; and the great Yerkes telescope of 40 inches in 
diameter, 40,000 times as much, or about 35,000 after allow- 
ing for the losses. The amount of light is proportional to 
the square of the diameter of the object-glass. 

The apparent brightness of an object which, like the moon 
or a planet, shows a disk, is not, however, increased in any 
such ratio, because the light gathered by the object-glass is 
spread out by the magnifying power of the eyepiece. But 
the total quantity of light in the image of the object greatly 
exceeds that which is available for vision with the naked 
eye, and objects which, like the stars, are mere luminous 
points have their brightness immensely increased, so that 
with the telescope millions otherwise invisible are brought 
to light. With the telescope, also, the brighter stars are easily 
seen in the daytime, 

406. The Achromatic Telescope. — A single lens cannot 
bring the rays which emanate from a single point in the object 
to any exact focus, since the rays of each different color are 
differently refracted, — the blue more than the green, and this 
more than the red. In consequence of this so-called " chro- 
matic aberration " the simple refracting telescope is a very 
poor 1 instrument. 

About 1760 it was discovered, in England, that by making 
the object-glass of two or more lenses of different kinds of 

1 By making it extremely long in proportion to its diameter, the indis- 
tinctness of the image is considerably diminished ; and in the middle of the 
seventeenth century instruments more than 100 feet in length were used 
by Huyghens and others. Saturn's rings and several of his satellites were 
discovered with instruments of this kind. 



TELESCOPES 365 

glass, the chromatic aberration can be nearly corrected. 
Object-glasses so made — none others are now in common 
use — are called achromatic. In practice, only two lenses are 
ordinarily used in the construction of an astronomical glass, 
— a convex of crown-gl&ss and a concave of flint-glass, the 
curves of the two lenses and the distances between them being 
so chosen as to give the best attainable correction of the 
" spherical " aberration (" Physics," page 363), as well as of 
the chromatic. 

407. Achromatism not Perfect. — It is not possible with 
the kinds of glass ordinarily obtainable to get a perfect cor- 
rection of color. Even the best achromatic telescopes show a 
purple halo around the image of a bright star, which, though 
usually regarded as " very beautiful " by tyros, seriously 
injures the definition and is especially obnoxious in large 
instruments. 

This imperfection of achromatism makes it impossible to get 
satisfactory photographs with an ordinary object-glass corrected for 
vision. An instrument for photography must have an object-glass 
specially corrected for the purpose, since the rays most efficient in 
impressing the image upon the photographic plate are the blue and 
violet rays, which in the ordinary object-glass are left to wander 
very wildly. By cutting off the violet and red rays with colored 
screens it is possible, however, to obtain very satisfactory photographs 
of bright objects like the moon, where loss of light is of no conse- 
quence. (See Sec. 156*.) 

Much is hoped from the new kinds of glass now made for optical 
purposes at Jena, Germany, as the results of the experiments con- 
ducted by Professor Abbe at the expense of the German government. 
A number of telescopes have already been made with a far better 
color correction than was formerly possible, so that they can be used 
for both visual and photographic work. 

408. Diffraction and Spurious Disks. — Even if a lens were 
absolutely perfect as regards the correction of aberrations, 



366 



APPENDIX 



Ramsden 
{Positive) 



Iluyghenian 
(Negative) 

'|| W^ — If 1 



both spherical and chromatic, it would still be unable to give 
vision absolutely distinct. Since light consists of waves of 
finite length, the image of a luminous point can never be also 
^ point, but must of mathematical necessity be a hazy-edged 
disk of finite diameter surrounded by a series of " diffraction " 
rings. The diameter of the " spurious disk " of a star, as it is 
called, varies inversely with the diameter of the object-glass : 
the larger the telescope, the smaller the image of a star with 
a given magnifying power. 

With a good telescope and a power of about 30 to the inch of 
aperture (120 for a 4-inch telescope) the image of a star, when the 
air is steady (a condition unfortunately seldom fulfilled), should be 

a clean, round disk with a bright 
ring around it, separated from the 
disk by a clear black space. 
According to Dawes, the disk of 
a star with a 41-inch telescope 
should be about 1" in diameter ; 
with a 9-inch instrument 0".5, 
and \" for a 36-inch glass. In a 
4^-inch telescope, therefore, the two disks of a double star with 
a distance of 1" between centers would be just in contact ; with the 
Yerkes telescope this would be the case if the distance were 0".l ; 
and in this fact lies much of the superiority of great telescopes. 

409. Eyepieces. — For some purposes the simple convex 
lens is the best " eyepiece " possible ; but it performs well 
only for a small object, like a close double star, placed exactly 
in the center of the field of view. Generally, therefore, we 
employ " eyepieces " composed of two or more lenses, which 
give a larger field of view than a single lens, and define satis- 
factorily over the whole extent of the field. They fall into 
two general classes, the positive and the negative. 

The positive eyepieces are much more generally useful. They act 
as simple magnify ing-glasses, and can be taken out of the telescope 



Fig. 100. — Telescope Eyepieces 



TELESCOPES 367 

and used as hand magnifiers if desired. The image of the object 
formed by the object-glass lies outside of this kind of eyepiece, between 
it and the object-glass. 

In the negative eyepiece, on the other hand, the rays from the 
object-glass are intercepted by the so-called " field-lens " before reach- 
ing the focus, and the image is formed between the two lenses of the 
eyepiece. It cannot, therefore, be used as a hand magnifier. 

Fig. 100 shows the two most usual forms of eyepiece, but there 
are many others. 

These eyepieces show the object in an inverted position ; but 
this is of no importance as regards astronomical observations. 

410. Reticle. — When the telescope is used for pointing 
upon an object, as it is in most astronomical instruments, it 
must be provided with a " reticle " of some sort. The simplest 
form is a metallic frame with spider lines stretched across it, 
the intersection of the spider lines being the point of reference. 
This reticle is placed not at or near the object-glass, as is 
often supposed, but in its focal plane, as ab in Fig. 99. Some- 
times a glass plate with fine lines ruled upon it is used 
instead of spider lines. Some provision must be made for 
illuminating the lines, or " wires/' as they are usually called, 
by reflecting into the instrument a faint light from a lamp 
suitably placed. 

411. The Reflecting Telescope. — About 1670, when the chro- 
matic aberration of refractors first came to be understood (in 
consequence of Newton's discovery of the " decomposition of 
light"), the reflecting telescope was invented. For nearly 
150 years it held its place as the chief instrument for star- 
gazing, until about 1820, when large achromatics began to 
be made. There are several varieties of reflecting telescope, 
differing in the way in which the image formed by the mirror 
is brought within reach of the magnifying eyepiece. 

Until about 1870 the large mirror (technically " speculum ") 
was always made of speculum metal, a composition of copper 



368 APPENDIX 

and tin. It is now usually made of glass, silvered on the 
front by a chemical process. When new, these silvered films 
reflect much more light than the old speculum metal : they 
tarnish rather easily, but fortunately can be easily renewed. 

412. Large Telescopes. — The largest telescopes ever made have 
been reflectors. At the head stands the enormous instrument of 
Lord Rosse of Birr Castle, Ireland, 6 feet in diameter and 60 feet 
long, made in 1842 and still used. Next in size, but probably superior 
in power, comes the 5-foot silver-on-glass reflector of Mr, Common, 
at Ealing, England, completed in 1889 ; and then follow a number 
(four or five) of 4 -foot telescopes, — that of Herschel (erected in 
1789, but long ago dismantled) being the first, while the great 
reflector at Paris is the only instrument of this size now in active 
use. The only large reflectors in the United States are the 3-foot 
Crossley reflector at the Lick Observatory, and a 2-foot instrument 
at the Yerkes. 

Of the refractors, the largest is that of the Yerkes Observatory at 
Lake Geneva, Wisconsin, with an object-glass 40 inches in diameter, 
and a tube nearly 70 feet long. The next in size is the telescope of 
the Lick Observatory, which has an aperture of 36 inches. Next 
to this come the great telescopes at Potsdam, Pulkowa, Meudon, 
and Nice, with apertures of about 30 to 31 inches ; the Greenwich 
telescope, 28 inches ; the Vienna telescope, 27 inches ; the two tele- 
scopes at Washington and the University of Virginia, 26^ inches ; 
and four or five others with apertures of from 26 to 23 inches, 
at Cambridge (England), Greenwich, Paris, and Princeton. More 
than half of these large object-glasses were made by the Clarks of 
Cambridge (U.S.). 

413. Relative Advantages of Reflectors and Refractors. — There 
is no little discussion on this point, each form of instrument having 
its earnest partisans. 

In favor of the reflector we have first, its cheapness and compara- 
tive ease of construction, since there is but one surface to grind and 
polish, as against four in an achromatic object-glass ; second, the fact 
that reflectors can be made larger than refractors ; third, the reflector 
is absolutely achromatic, and this gives it an immense advantage in 



THE EQUATORIAL 



369 



certain lines of astronomical photography (as, for instance, in that 
of the nebulae) and of spectroscopy. 

On the other hand, a refractor gives a much brighter image than 
a reflector of the same size ; it also generally defines much better, 
because, for optical reasons into which we cannot enter here, any 
slight distortion or malformation of the speculum of a reflector dam- 
ages the image many times more than the same amount of distortion 
of an object-glass. Then a lens hardly deteriorates at all with age, 
while a speculum soon tarnishes, and must be resilvered or repolished 
every few years. The lens gives also a 
wider field of good definition. 

Finally, as a rule, refractors are 
lighter and more convenient than reflect- 
ors of equal power. 

414. Mounting of a Telescope, 
— the Equatorial. — A telescope, 
however excellent optically, is not 
of much use unless firmly and con- 
veniently mounted. 1 

At present some form of equatorial 
mounting is practically universal. 
Fig. 101 represents schematically 
the ordinary arrangement of the 
instrument. Its essential feature 
is that its " principal axis " (i.e., the 
one which turns in fixed bearings attached to the pier, and is 
called the polar axis) is placed parallel to the earth's axis, 
pointing to the celestial pole, so that the circle H, attached to 
it, is parallel to the celestial equator. This circle is some- 
times called the hour-circle, sometimes the right-ascension 

1 We may add that it must, of course, be mounted where it can be 
pointed directly at the stars, without any intervening window-glass 
between it and the object. We have known purchasers of telescopes to 
complain bitterly because they could not see Saturn well through a closed 
window. 




Fig. 101. — The Equatorial 



370 



APPENDIX 







Fig. 102. — Great Double Equatorial, Visual and Photographic, of the 
Potsdam Astrophysical Observatory 

circle. At the extremity of the polar axis a " sleeve " is 
fastened, which carries within it the declination axis D, and 
to this declination axis is attached the telescope tnbe T, and 
also the declination circle C. 



THE MICROMETER 



371 



The advantages of this mounting are very great. In the 
first place, when the telescope is once pointed upon an object 
it is not necessary to move the declination axis at all in order 
to keep the object in the field, but only to turn the polar axis 
with a perfectly uniform motion, which motion can be, and 
usually is, given by clockwork (not shown in the figure). 

In the next place, it is very easy to find an object even 
if invisible to the eye (like a faint comet, or a star in the 




Fig. 103. — Filar-Position Micrometer 
By Warner and Swasey 

daytime) provided we know its right ascension and declination, 
and have the sidereal time, — a sidereal clock or chronometer 
being an indispensable accessory of the instrument. 

Fig. 81, Sec. 337, represents another form of equatorial mounting, 
which has been adopted for some of the instruments of the photo- 
graphic campaign. 

415. The Micrometer. — This is an instrument for meas- 
uring small angles, usually not exceeding 15' or 20'. Various 



372 



APPENDIX 



2 



i~J 



kinds are employed, all of them small pieces of apparatus, 
which, when used, are secured to the eye end of a telescope. 
The most common is the parallel-wire micrometer, which is a 

pair of parallel spider threads, 
one or both of which can be 
moved with a fine screw with 
a graduated head, so that the 
distance between the two 
"wires" can be varied at 
pleasure and then " read off " 
by looking at the micrometer 
head. Fig. 103 represents such 
an instrument to be attached 
to a telescope ; the threads 
are in the box BB, and are 
viewed through the eyepiece. 
416. The Transit-Instru- 
ment (Fig. 104). — This con- 
sists of a telescope carrying at the eye end a reticle, and 
mounted on a stiff axis with pivots 
that are perfectly equal and cylindri- 
cal. They turn in Y's which are 
firmly set upon some sort of frame- 
work or on the top of solid piers, and 
so placed that the axis will be exactly 
east and west and precisely level. 
When the telescope is turned on its 
axis, the middle "wire " of the reticle, 
if everything is correctly adjusted, 
will follow the celestial meridian, 
and whenever a star crosses the wire 

we know that it is exactly on the meridian. Instead of a 
single wire the reticle generally contains a number of wires 
equally spaced, as shown in Fig. 105. The observer notes 



Fig. 104. — The Transit-Instrument 




Fig. 105. — Reticle of the 
Transit-Instrument 



TIMEPIECES 373 

by his timepiece the instant at which the object crosses 

each of the wires, and the mean of the observations is taken 

as giving the moment when the star crossed the middle 

wire. 

A delicate spirit-level, to be placed on the pivots and test 

the horizontality of the axis, is an indispensable accessory. 

So far as the theory of the instrument is concerned, a gradu- 
ated circle is not essential ; but practically it is necessary to 
have one attached to the axis in order to enable the observer 
to set the instrument to the proper altitude in preparing for 
the observation of a star. 

417. The Astronomical Clock, Chronometer, and Chrono- 
graph. — A good timepiece is an essential adjunct of the 
transit-instrument, and equally so of most other astronom- 
ical instruments. The invention of the pendulum clock by 
Huyghens was almost as important an event in the history 
of practical astronomy as that of the telescope itself. 

The astronomical clock differs in no essential respect from 
any other, except that it is made with extreme care and has a 
" compensated " pendulum so constructed that the rate of the 
clock will not be affected by changes of temperature. It is 
almost invariably made to beat seconds, and usually has its 
face divided into twenty-four hours instead of twelve. 

Excellence in a clock consists essentially in the constancy 
of its "rate" ; i.e., it should gain or lose precisely the same 
amount each day, and as a matter of convenience the daily 
rate should be small, not to exceed a second or two. The 
rate is adjusted by slightly raising or lowering the pendulum 
bob, or putting little weights upon a small shelf attached to 
the rod; the " error," when necessary, is corrected by simply 
setting the hands. 

The error of a timepiece is the difference between the time shown 
by the clock-face and the true time at the moment ; the rate is the 
amount it gains or loses in twenty-four hours. 



374 



APPENDIX 



The chronometer is simply a carefully made watch and 
has the advantage of portability, though in accuracy it 
cannot quite compete with a well made clock. 

Formerly transit-instrument observations were made by 
simply noting with eye and ear the time indicated by the 

clock at the moment when 
the star observed was 
crossing the wire or reti- 
cle. A skillful observer 
can do this within about 
a tenth of a second. At 
present the observer usu- 
ally presses a telegraph- 
key at the moment of the 
transit and so telegraphs 
the instant to an instru- 
ment called a chronograph, 
which makes a permanent 
record of the observation 
upon a sheet of paper, — 
thus making the observa- 





Fig. 106. — The Meridian Circle (schematic) 

tion much more accurate as well as easier 



For the description of the Chronograph, see General Astronomy, 
Art. 56, or Manual, Sec. 59. 

418. The Meridian Circle, or Transit Circle. — In many 
respects this is the fundamental instrument of a working 
observatory. It is simply the transit-instrument plus a finely 
graduated circle or circles attached to the axis and provided 
with microscopes for reading the graduation with precision. 
In the accurate construction of the pivots of the instru- 
ment and of the circles, with their graduation, the utmost 
resources of the mechanical art are taxed. Fig. 107 shows 



THE MERIDIAN CIRCLE 



375 



the instrument in principle. Fig. 107 represents the new 
meridian circle of the Washington Observatory with its acces- 
sories. It has a telescope of 6 inches aperture and circles 
27 inches in diameter. 




Fig. 107. — Transit, or Meridian, Circle in United States Naval Observatory 

at Washington 
By Warner and Swasey 



Its main purpose is to determine the right ascension and 
declination of objects as they cross the meridian. The 
declination is determined by measuring how many degrees 



376 APPENDIX 

the object is north or south of the celestial equator at the 
moment of transit. The " circle-reading " for the equator 
must first be determined as a zero point ; and this is done by 
observing a star near the pole and getting the circle-reading as 
it crosses the meridian above the pole, and, twelve hours later, 
when it crosses again below it. The mean of these two read- 
ings, corrected for refraction, will be the circle-reading for 
the pole, or the polar point, which is, of course, just 90° from 
the equatorial zero point. 

419. The Nadir Point. — To get the latitude of the observer 
with this instrument (Sec. 81) it is necessary also to have 
the nadir point as a zero, i.e., the circle-reading which corre- 
sponds to the vertical position of the telescope. This is 
found by pointing the telescope down towards a basin of 
mercury beneath it, and setting it so that the image of the 
east and west wire in the reticle coincides with itself. Then 
the telescope will be exactly vertical. The horizontal point 
is just 90° from the nadir point, and the difference between 
the (north) horizontal point and the polar point is the latitude 
of the observatory. 

Obviously the instrument can also be used as a simple 
transit-instrument in connection with a clock, so that (Sec. 99) 
the observer can determine at one observation both the right 
ascension and declination of any object which is visible when 
it crosses the meridian. 

420. The Sextant. — All the instruments so far mentioned, 
except the chronometer, require firmly fixed supports, and 
are, therefore, useless at sea. The sextant is the only instru- 
ment for measurement upon which the mariner can rely. By 
means of it he can measure the angular distance between any 
two points (as, for instance, the sun and the visible horizon), 
not by pointing first on one and afterwards on the other, but 
by sighting them both simultaneously and in apparent coinci- 
dence. This observation can be accurately made even if he 



THE SEXTANT 



377 



has no stable footing, but is swinging about on the deck of a 
vessel. Fig. 108 represents the instrument. (For a detailed 
description and explanation, see General Astronomy, Arts. 
76-80, or Manual, Sees. 73-75.) 

421. Use of the Instrument. — The principal use of the 
instrument is in measuring the altitude of the sun. At sea, 
an observer holding the instrument in his right hand and 




Fig. 108. — The Sextant 



keeping the plane of the arc vertical, looks directly towards 
the visible horizon through the horizon-glass, H, at the point 
under the sun. Then by moving the index, N, with his left 
hand, he inclines the index mirror upward until he sees the 
reflected image of the sun, and the lower edge of this image is 
brought to touch the horizon line. The reading of the gradu- 
ation, after due correction for refraction, etc., gives the sun's 
true altitude at the moment. If the observation is made very 



378 APPENDIX 

near noon, for the purpose of determining the latitude, it will 
not be necessary to read the chronometer at the same time. 
If, however, the observation is made for the purpose of deter- 
mining the longitude (Sec. 497), the instant of observation, as 
shown by the chronometer, must be carefully noted. 

The skillful use of the sextant requires considerable dex- 
terity, and from the small size of the telescope the angles 
measured are less precisely measured than with large fixed 
instruments; but the portability of the instrument and its 
applicability at sea render it absolutely invaluable. It was 
invented by Gregory of Philadelphia, in 1730, but an earlier 
design of an instrument on the same principle has since been 
found among the unpublished papers of Newton. 



MISCELLANEOUS 

Hour- Angle and Time — Twilight — Determination of Latitude — Ship's Place 
at Sea — Finding the Form of the Earth's Orbit — The Ellipse — Illustra- 
tions of Kepler's Third Law — The Equation of Light and the Sun's Dis- 
tance — Aberration of Light — De l'lsle's Method of getting the Solar 
Parallax from the Transit of Venus — The Conic Sections — Stellar 
Parallax 

422. Hour-Angle and Time (supplementary to Sees. 89-91). 
— There is another way of looking at the matter of time 
which has great advantages. If we face towards the north 
pole and consider the star m (Fig. 109) as carried at the end 
of the arc mP of the hour-circle which connects it to the pole, 
we may regard this arc as a sort of clock-hand ; and if we 
produce it to the celestial equator and mark off the equator 
into 15°-spaces, or "hours," the angle mQP, or the arc QY, 
will measure the time which has elapsed since m was on the 
meridian PQ. The angle mPQ is called the hour-angle of the 
star m. It is the angle at the pole between the meridian and 
the hour-eircle which passes through the body. 



HOUR-AXGLE AND TWILIGHT 



379 



Having now this definition of the hour-angle, we may 
define sidereal time (Sec. 91) at any moment as the hour-angle 
of the vernal equinox at that moment. In the same way, the 
apparent solar time (Sec. 88) is the hour-angle of the sun's 
center ; the mean solar time (Sec. 89) is the hour-angle of a 
fictitious sun which moves around the heavens uniformly, once 
a year, in the equator, keeping its right ascension equal to 
the mean longitude of the real sun. For some purposes, as 
in dealing with the tides, 
it is convenient to use 
lunar time, which is sim- 
ply the hour-angle of the 
moon at any moment. 

423. Twilight is caused 
by the reflection of sunlight 
from the upper portions of 
the earth's atmosphere. After 
the sun has set, its rays still 
continue to shine through the 
air above the observer's head, 
and twilight continues as long 
as any portion of this illu- 
minated air can be seen from 

where he stands. It is considered to end when stars of the sixth 
magnitude become visible near the zenith, which does not occur 
until the sun is about 18° below the horizon ; but this is not strictly 
the same for all places. 

The duration of twilight varies with the season and with the 
observer's latitude. In latitude 40° it is about ninety minutes on 
March 1 and October 12, but more than two hours at the summer 
solstice. In latitudes above 50°, when the days are longest, twilight 
never quite disappears, even at midnight, and in latitude 60° one 
can read fair-sized type all night long. On the mountains of 
Peru, on the other hand, it is said never to last more than half 
an hour. 




Fig. 109. — Hour- Angle 



380 APPENDIX 

424. Methods of determining Latitude by Other Obser- 
vations than those of Circumpolar Stars (supplementary to 
Sec. 81). — To determine the latitude by observations of a cir- 
cumpolar star, the observer must remain at the same station 
at least twelve hours. The latitude can be determined, how- 
ever, with a good instrument, with almost equal precision by 
observing the meridian altitude, or zenith distance, of a body 
whose declination is accurately known. In Fig. 110 the circle 
SQPN is the meridian, Q and P being respectively the equa- 
tor and the pole, and Z the zenith. QZ is evidently the 
declination of the zenith (i.e., the distance of the zenith from 
the celestial equator) and is equal to PB, the latitude of the 
observer, or height of the pole. Suppose now that we observe 
Zs, i.e., the zenith distance of the star s, south of the zenith, 

as it crosses the meridian, and 
s- — i — ^* that we know Qs, the decima- 

ls* 3 tion of the star. Evidently 
/ \ QZ = Qs + sZ ; i.e., the latitude 
/ \ equals the declination of the star 

\2j plus its zenith distance. If the 

star were at s', south of the 
Fig. 110. -Determination of equator, the same equation would 
Latitude > 

hold good algebraically, because 

the declination, Qs 1 , is a minus quantity. If the star were at 
n, between the zenith and the pole, we should have : latitude 
equals the declination of the star minus the zenith distance. 

This is the method actually used at sea (Sec. 426), the sun being 
the object observed. 

There are many other methods in use, as, for instance, that 
by the zenith telescope and that by the prime-vertical instru- 
ment, which are practically more convenient and more accu- 
rate than either of the two described, but they are more 
complicated and their explanation would take us too far. 



MARINE ASTRONOMY 381 

FINDING THE PLACE OF A SHIP 

425. The determination of the place of a ship at sea is, 
from the economic point of view, the most important problem 
of Astronomy. National observatories and nautical almanacs 
were established, and are maintained principally to supply 
the mariner with the data needed to make this determination 
accurately and promptly. The methods employed are neces- 
sarily such that the required observations can be made with 
the sextant and chronometer, since fixed instruments, like the 
transit-instrument and meridian circle, are obviously out of 
the question on board a vessel. 

426. Latitude at Sea. — This is obtained by observing with 
the sextant the sun's maximum altitude, which is reached 
when the sun is crossing the meridian. 

Since at sea the sailor seldom knows beforehand the precise 
time which will be shown by his chronometer at noon, he 
takes care not to be too late, and begins to measure the sun's 
altitude a little before noon, repeating his observations every 
minute or two. At first the altitude will keep increasing, but 
when noon comes the sun will cease rising, and then begin to 
descend. The observer uses, therefore, the maximum altituue 
obtained, which, with due allowance for refraction and some 
other corrections (for details, see larger works), gives him the 
true altitude of the sun's center. Taking this from 90°, we 
get its zenith distance. 

Referring now to Fig. 110, in which the circle SQZPN is 
the meridian, P the pole, Z the zenith, and OQ the celestial 
equator seen edgewise, we see that PN, the altitude of the pole, 
is necessarily equal to ZQ, the distance from the zenith to the 
equator. Now, from the almanac, we find Qs, the declination 
of the sun for the time when the observations are made. 1 

1 If the sun happened to be south of the equator (in the winter), as at 
s', we should have ZQ equals Zs — s'Q. 



382 APPENDIX 

We have only to add to this Zs, the distance of the sun from 
the zenith (i.e., 90° — Ss, the observed altitude of the sun), to 
obtain QZ, which is the observer's latitude. 

It is easy in this way, with a good sextant, to get the lati- 
tude within about half a minute of arc, or, practically, about 
half a mile, which is quite sufficiently accurate for nautical 
purposes. 

427. Determination of Local Time and Longitude at Sea. 
— The usual method now employed for the longitude depends 
upon the chronometer. This is carefully " rated " in port ; 
i.e., its error and its daily gain or loss are determined by com- 
parisons with an accurate clock for a week or two, the clock 
itself being kept correct to Greenwich time by transit obser- 
vations. By merely allowing for the gain or loss since leaving 
port, and adding this gain or loss to the " error " (Sec. 417) 
which the chronometer had when brought on board, the sea- 
man at once obtains the error of the chronometer on Green- 
wich time at any moment ; and allowing for this error, he has 
the Greenwich time itself with an accuracy which depends 
only on the constancy of the chronometer's rate : it makes no 
difference whether it is gaining much or little, provided its 
daily rate is steady. 

He must also determine his own local time; and this must 
be done with the sextant, since, as was said before, an instru- 
ment like the transit cannot be used at sea. He does it by 
measuring the altitude of the sun, not at or near noon, as often 
supposed, but when the sun is as near due east or west as cir- 
cumstances permit. From such an observation the sun's hour- 
angle, i.e., the apparent solar time (Sec. 422), is easily found 
by a trigonometrical calculation, provided the ship's latitude 
is known. (For the method of calculation, see General 
Astronomy, Art. 116, or Manual, Sec. 103.) 

The longitude follows at once, being simply the difference 
between the Greenwich time and the local time. 



FORM OF THE EARTH'S ORBIT 



383 



In certain cases where the chronometers have been for 
some reason disturbed, the mariner is obliged to get his Green- 
wich time by observing with a sextant the distance of the 
moon from some star or planet near the ecliptic, but the 
results thus obtained are comparatively inaccurate. 

428. To find the Form of the Earth's Orbit (supplementary 
to Sec. 119). — Take the point S (Fig. Ill) for the sun, and 
draw from it a line, SO, directed towards the vernal equinox 
from which longitudes are measured. Lay off from S lines 
indefinite in length, making angles with SO equal to the 
earth's longitude as seen 
from the sun on each 
of the days when the 
observations are made 
(earth's longitude equals 
sun's longitude + 180°). 
We shall thus get a sort 
of "spider" showing the 
direction of the earth as 
seen from the sun on 
each of those days. 

Next, as to the dis- 
tances. While the ap- 
parent diameter of the 
sun does not tell us its absolute distance from the earth, unless 
we know his diameter in miles, yet the changes in the appar- 
ent diameter do inform us as to the relative distance at 
different times, since the nearer we are to the sun, the larger 
it looks. If, then, on the legs of the " spider " we lay off dis- 
tances inversely proportional 1 to the number of seconds of arc 
in the sun's measured diameter at each date, these distances 
will be proportional to the true distance of the earth from the 

10000" 




Fig. 111. — Determination of the Form 
of the Earth's Orbit 



1 I.e. 1 lay off S u S 2 , etc., each equal to 



diameter 



384 



APPENDIX 



sun, and the curve joining the points thus obtained will be a 
true map of the earth's orbit, though without any scale of 
miles. When the operation is performed we find that the 
orbit is an ellipse of small eccentricity with the sun in one 
of the two foci. 

429. The Ellipse, and Definitions relating to it (supplemen- 
tary to Sees. 119, 120). — If we drive two pins into a board, 
as at F and S in Fig. 112, and put around the pins a looped 
thread, attached to the point of a pencil, P, then, on carrying 
the pencil around, it will mark out an ellipse. The pins, F 

and S, are the " foci " of the 
ellipse and C is its center. 
From the manner in which 
the ellipse is constructed it 
is clear that at any point, P, 
on its outline, the sum of 
the two lines PS and PF will 
always be the same, and equal 
to the line ^4^4'. The length 
of the ellipse, ^4.4', is called 
its major axis, and AC its sewu'-major axis, which is usually 
designated by a, while the semi-minor axis, BC, is lettered b. 
CS 







Fig. 112. — The Ellipse 



The fraction, 



AC 



is called the eccentricity of the ellipse and 



determines the shape of the oval. Its usual symbol is e. If e 
is nearly unity, i.e., if CVS is nearly equal to CA, the oval 
will be very narrow compared with its length ; but if CS is 
very small compared with CA, the ellipse will be almost round. 
Taken together, a and e determine the size and form of the 
oval. The ellipse is called a " conic " because when a cone is 
cut across obliquely the section is an ellipse. (See Sec. 440.) 

430. Problems illustrating the " Harmonic Law " (supplementary 
to Sec. 220). — To aid the student in apprehending the scope of 
Kepler's third law, we give a few examples of its application. 



PROBLEMS 385 

1. What would be the period of a planet having a mean distance 
from the sun of one hundred astronomical units, i.e., a distance a 
hundred times that of the earth? 

I 3 : 100 3 = l 2 (year) : X 2 ; 
whence X (in years) = VlOO 3 = 1000 years. 

2. What would be the distance from the sun of a planet having a 
period of 125 years ? 

3 , 

l 2 (year) : 12 5 2 — l 3 : X 3 ; whence X = V125 2 = 25 astron. units. 

3. What would be the period of a satellite revolving close to the 
earth's surface ? 

(Moon's Dist.) 3 : (Dist. of Satellite) 3 = (27.3 days) 2 : X\ 
or, 60 3 : l 3 = 2T.3 2 : X 2 ; 

whence X = '_f. days = d .587 = l h 24 m .5. 
V60 3 

4. How much would an increase of 10 per cent in the earth's 
distance from the sun lengthen the year ? 

100 3 
X being the new length of the year. X is found by computation 
(most conveniently by the help of logarithms) to be 421.38 days. 
The increase is 56.13 days. 

5. What is the distance from the sun of an asteroid with a period 
of 3 J years? 

I 2 (year) : 3.5 2 = l 3 : Dist. 3 

•.• Dist. = V(3.5) 2 = -\/l2.25 = 2.305 astron. units. 

431. The Equation of Light. — When we observe a celestial 
body, w r e see it not as it is at the moment of observation, but 
as and where it was at the moment when the light which we 
see left it. If we know its distance in astronomical units 
and know how long light takes to traverse that unit, we can 
at once correct our observation by simply dating it back to 
the time when the light started from the object. The neces- 
sary correction is called the "equation of light " and the time 



386 APPENDIX 

required by light to traverse the astronomical unit of distance 
is called the " Constant of the Light- Equation " (not quite 500 
seconds, as we shall see). 

It was in 1675 that Roemer, the Danish astronomer (the inventor 
of the transit-instrument, meridian circle, and prime-vertical instru- 
ment, — a man almost a century in advance of his day), found that 
the eclipses of Jupiter's satellites show a peculiar variation in their 
times of occurrence, which he explained as due to the time taken by 
light to pass through space. His bold and original suggestion was 
neglected for more than fifty years, until long after his death, when 
Bradley's discovery of aberration (Sec. 435) proved the correctness 
of his views. 

432. Determination of the Constant of the Equation of 
Light. — Eclipses of the satellites of Jupiter recur at intervals 
which are really almost exactly equal (the perturbations being 
very slight), and the interval can easily be determined and the 
times tabulated. But if we thus predict the times of the 
eclipses during a whole synodic period of the planet, then, 
beginning at the time of opposition, it is found that as the 
planet recedes from the earth the eclipses, as observed, fall 
constantly more and more behindhand and by precisely the 
same amount for all four satellites. The difference between 
the predicted and observed time continues to increase until 
the planet is near conjunction, when the eclipses are about 
16 m 38 8 later than the prediction. After the conjunction they 
quicken their pace and make up the loss, so that when oppo- 
sition is reached once more they are again on time. 

It is easy to see from Fig. 113 that at opposition the planet 
is nearer the earth than at conjunction by just two astronom- 
ical units. At opposition the distance between Jupiter and 
the earth is JA, while six and a half months later, at the 
time of Jupiter's superior conjunction, it is JB. The differ- 
ence between JA and JB is just twice the distance from S 
to A. 



THE EQUATION OF LIGHT 



387 



The whole apparent retardation of eclipses between opposi- 
tion and conjunction must therefore be exactly twice the time 1 
required for light to come from the sun to the earth. In this 
way the " light-equation constant " is found to be very nearly 
499 seconds, or 8 minutes 19 seconds, with a probable error 
of perhaps two seconds. 

433. Since these eclipses are gradual phenomena, the determina- 
tion of the exact moment of a satellite's disappearance or reappear- 
ance is very difficult, and this 

renders the result somewhat ^-\vcy v ™' w ^'Oz/^ 

uncertain. Professor E. C. 
Pickering of Cambridge has 
proposed to utilize photometric 
observations for the purpose 
of making the determination 
more precise, and two series 
of observations of this sort, 
and for this purpose, have 
been made during the last 
sixteen years, — one in 
Cambridge, U.S., and the 
other at Paris under the direc- 
tion of Cornu, who devised a 
similar plan. They are now 
under discussion but the result has not yet been published. 

Pickering has also applied photography to the observation of these 
eclipses with encouraging success. 

434. The Distance of the Sun determined by the " Light- 
Equation/ ' — Until 1849, when Fizeau first succeeded in actu- 
ally measuring it, our only knowledge of the velocity of light 

1 The student's attention is specially directed to the point that the 
observations of the eclipses of Jupiter's satellites give directly neither the 
velocity of light nor the distance of the sun ; they give only the time 
required by light to make the journey from the sun. Many elementary 
text-books, especially the older ones, state the case carelessly. 




Fig. 113. — The Equation of Light 



388 



APPENDIX 



was obtained from such observations of Jupiter's satellites. 
By assuming as known the earth's distance from the sun, the 
velocity of light can be obtained when we know the time 
occupied by light in coming from the sun. 

At present, however, the case is reversed. We can deter- 
mine the velocity of light by two independent experimental 
methods, and with a surprising degree of accuracy. Then, 
knowing this velocity and the " light-equation constant," we 
can deduce the distance of the sun. According to the latest 
determinations the velocity of light is 186,330 miles per 

second. Multiplying this 
by 499, we get 92,979000 
miles for the sun's distance. 
(Compare Sec. 436.) 

435. Aberration of 
Light. — The fact that 
light is not transmitted 
instantaneously causes the 
apparent displacement of 
an object viewed from any 
moving station, unless the 
motion is directly towards 
or from that object. If the motion of the observer is not 
rapid, this displacement, or " aberration," is insensible; but 
the earth moves so swiftly in its orbit (18-J- miles per second) 
that it is easily observable in the case of the stars. Astro- 
nomical aberration may be defined, therefore, as the apparent 
displacement of a heavenly body due to the combination of the 
orbital motion of the earth tvith that of light — the direction 
in which we have to point our telescope in observing a star 
is not the same as if the earth were at rest. 

We may illustrate this by considering what would happen in the 
case of falling raindrops. Suppose the observer standing with a 
tube in his hand while the drops are falling straight down : if he 




Fig. 114. — Aberration 



ABERRATION 389 

wishes to have the drops descend through the middle of the tube 
without touching the sides, he must keep it vertical so long as he 
stands still ; but if he advances in any direction the drops will strike 
the side of the tube, and he must thrust forward its upper end 
(Fig. 114) by an amount which equals the advance he makes while 
a drop is falling through it ; i.e., he must incline the tube forward at 
an angle depending both upon the velocity of the raindrop and the 
swiftness of his own motion, so that when the drop, which entered 
the tube at B, reaches A 1 , the bottom of the tube will be there also. 
It is true that this illustration is not a demonstration, because light 
does not consist of particles coining towards us, but of waves trans- 
mitted through the ether of space. But it has been shown (though 
the proof is by no means elementary) that within very narrow limits 
the apparent direction of a wave is affected in precisely the same way 
as that of a moving projectile. 

Observations on several hundred stars show that a star situ- 
ated on a line at right angles to the direction of the earth's 
motion is thus apparently displaced by an angle of about 20". 5. 

This is the so-called " Constant of Aberration." 

The Pulkowa observations give 20".493 ; but according to 
Chandler the most recent determinations (1903) will probably 
carry it up to about 20 ".52. 

If the star is in a different part of the sky its displacement 
will be less, the amount being easily calculated when the date 
and the star's position are given. 

436. Determination of the Sun's Distance by Means of the 
Aberration of Light. — The constant of aberration, a, and 
the two velocities, that of the earth in its orbit, u, and the 
velocity of light, V, are connected by the very simple equation 

a = 206,265 x - ; whence u = 206 265 X V. 

When, therefore, we have ascertained the value of a (20 ".52) 
from observations of the stars, and of V (186,330 miles, accord- 
ing to the most recent determinations by Michelson and 



390 APPENDIX 

Newcomb) by physical experiments, we can immediately find 
u, the velocity of the earth in her orbit. The circumference of 
the earth's orbit is then found by multiplying this velocity, u, 
by the number of seconds in a sidereal year (Sec. 127) ; and 
from this we get the radius of the orbit, or the earth's mean 
distance from the sun, by dividing the circumference by 2ir 
(tt = 3.14159). Taking a = 20".52, the mean distance of the 
sun comes out 93,104000 miles. 

But the uncertainty of a is probably as much as 0".03, and 
this affects the distance proportionally, say one part in 600, 
or 150,000 miles. Still, the method is one of the very best 
of all that we possess for determining in miles the value of 
"the Astronomical Unit." 

437. De PIsle's Method of determining the Sun's Parallax 
by a Transit of Venus. — We have thus (Sees. 434 and 436) 
two methods by which the mean distance of the sun from the 




Fig. 115. — Transit of Venus 

earth can be determined. They both depend upon a knowl- 
edge of the velocity of light, and, of course, were unavailable 
before 1849, when Fizeau first succeeded in actually measuring 
it. Before that time it was necessary to rely entirely upon 
observations of either Mars or Venus, made at times when 
they come specially near us. 

Most of the methods of getting the sun's parallax and dis- 
tance from such observations depend upon our having a pre- 
vious knowledge of the relative distances of the planets from 
the sun. These relative distances were ascertained centuries 



TRANSITS OF VENUS 391 

ago. Copernicus knew them nearly as accurately as we have 
them now ; but since we have not explained in this book how 
they are found (the explanation involves a little Trigonom- 
etry), we limit ourselves to giving here a single very simple 
method, which requires a previous knowledge not of the rela- 
tive distances of Venus and the earth from the sun, but only 
of the synodic period of the planet (Sec. 228), i.e., the time in 
which she gains one entire revolution upon the earth. This 
is almost exactly 584 days (583.971), as has been known from 
remote antiquity. 

Fig. 115 represents things at a transit of Venus as they 
would be seen by one looking down from an infinitely distant 
point above the earth's north pole. 
As seen from the earth itself, 
Venus would appear to cross the 
sun, striking the disk on the east . 
side and moving straight across to 
the west, making four " contacts " 
with the edge of the sun, as shown 
in Fig. 116. 

438. Suppose, now, that two 

observers, E and W (Fig. 114), - . ■ 

, . Fig. 116. — Contacts in a Transit 

are stationed opposite each other of Venus 

and near the earth's equator. 

E will see Venus strike the sun's disk before W does, and if 

they both observe the moment of contact in Greenwich time, 

the difference between their records will be the time it takes 

Venus to move over the arc from V x to F 2 . From the figure 

it is clear that the angle ViDV% is the same as EDW, the 

earth' } s apparent diameter seen from the sun, and this is at once 

known when we have the time from V x to V 2 . 

Since Venus gains one revolution in 584 days, in one day 

she will gain F | ? of a revolution, or 37' (very nearly), and 

this will make her gain 1".54 in one minute. Now it is found 




392 



APPENDIX 



that the difference between the moments of contact at two 
stations situated like E and W is about ll m 25 s , and hence 
that the diameter of the earth, as seen from the sun, is 17".6, 
or the sun's horizontal parallax (Sec. 139) is 8 ".8 ; from which 
its distance is easily found (Sec. 140). 

The reader will see that the two observers must know their 
longitudes accurately in order to be sure of the correct Green- 
wich time. Moreover, the two stations can never be quite 

exactly opposite 
each other, but 
stations a little 
nearer together 
must be taken 
and proper al- 
lowances made. 
Finally, we are 
very sorry to 
add that the 
necessary obser- 
vations of the 
moment when 
Venus reaches 
the edge of the 
sun's disk can- 
not be made 
with the accu- 
racy which is desirable, owing to the effect of the planet's 
atmosphere (see Sec. 248) ; so that practically the method 
is less accurate than might be hoped. (For further details, 
see General Astronomy, Chap. XVI.) 

439. The Parabola (supplementary to Sees. 292-298).- 
Tliis differs from the ellipse in never coming around into itself. 
In Fig. 117, the curves PA ly 7M 2 , and PA 3 are ellipses of dif- 
ferent length, all having S at one of their foci, but having F 1} 




Fig. 117. — Ellipse, Parabola, and Hyperbola 



THE CONICS 



393 



F 2 , and F z at the other. The first and smallest of the ellipses 
is nearly circular and shaped about like the orbit of Mercury, 
the two foci S and F x being pretty near together ; the next is 
more eccentric than the orbit 
of any asteroid ; and the third 
still more so, about like the 
orbit of Halley's comet. Now, 
if we imagine the point F car- 
ried farther and farther to the 
right the ellipse will grow 
larger and longer, until when 
F is infinitely far away the 
curve will become a parabola. 

Of course if the point F is 
very distant, even if not infi- 
nitely so, the part of the curve 
near S will agree with the parab- 
ola so closely that no one could 
distinguish between them. 

All ellipses that have S for 
the focus and P for the peri- 
helion lie inside of the parab- 
ola, while another set of 
conic curves called hyperbolas, 
with the same focus and peri- 
helion, lie entirely outside of 
it, which is, so to speak, a sort 
of boundary or division line 
between the ellipses and 
hyperbolas which have this 
focus and perihelion. 

440. The Conic Sections. — The way in which these curves 
— the ellipse, parabola, and hyperbola — are formed by sec- 
tions of the cone is shown by Fig. 118. 




Fig. 118. — The Conies 



394 APPENDIX 

(a) If the cone be cut by a plane which makes with its 
axis, VC, an angle greater than BVC, the plane of the section 
will cut completely across the cone and the section EF will 
be an ellipse, which will vary in shape and size according to 
the position of the plane. The circle is simply a special case 
when the cutting plane is perpendicular to the axis, as NM. 

(b) When the cutting plane makes with the axis an angle 
less than BVC (the semi-angle of the cone), it plunges contin- 
ually deeper and deeper into the cone and never comes out on 
the other side (the cone is supposed to be indefinitely pro- 
longed). The section in this case is an hyperbola, GHK. If 
the plane of the section be produced upward, however, it 
encounters the " cone produced/' cutting out from it a second 
hyperbola, G'H'K', precisely like the original one, but turned 
in the opposite direction. 

The axis of the hyperbola is always reckoned as negative, 
lying outside of the curve itself; in the figure, it is the line 
HH\ The center of the hyperbola is the middle point of this 
axis, a point also outside of the curve. 

(e) When the angle made by the cutting plane with the 
axis is exactly equal to the cone's semi-angle, the plane will 
be parallel to the side of the cone, and we then get the special 
case of the parabola, RPO, which forms a partition, so to 
speak, between the infinite variety of ellipses and hyperbolas 
which can be cut from a given cone. All parabolas are of the 
same shape, just as all circles are, differing only in size. The 
fact is by no means self-evident and we cannot stop to prove 
it, but it is true. 

441. Determination of the Parallax of a Star (supple- 
mentary to Sec. 343). — The determination of the parallax of 
stars had been attempted over and over again from the time of 
Tycho ]>rahe down, but without success until, in 1838, Bessel 
at last demonstrated and measured the parallax of 61 Cygni ; 
and the next year Henderson, of the Cape of Good Hope, 



STELLAR PARALLAX 395 

determined that of Alpha Centauri. The operation of measur- 
ing the parallax of a star is, on the whole, the most delicate 
in the whole range of practical Astronomy. Two methods have 
been used so far, known as the absolute and the differential. 

442. The Absolute Method consists in making the most 
scrupulously precise observations of the star's right ascension 
and declination with the meridian circle at different times 
through the course of an entire year, applying rigidly all 
known corrections (for precession, aberration, proper motion, 
etc.), and then examining the deduced positions. If the star 
is without parallax, these positions will all agree. If the star 
has a sensible parallax, they will show, on the other hand, 
when plotted on a chart, an apparent annual orbital motion of 
the star in a little ellipse, the major axis of which is twice the 
star's annual parallax, as can easily be shown. 

Theoretically, the method is perfect : practically, it seldom 
gives satisfactory results, because the annual changes of tem- 
perature and moisture disturb the instrument in such a way 
that the instrumental errors intertwine themselves with the 
parallax of a star in a manner that defies disentanglement. 
Ko process of multiplying observations and taking averages 
helps the matter very much, because the instrumental errors 
are themselves periodic annually, just as is the parallax ; still, 
in a few cases the method has proved successful, as in the 
case of Alpha Centauri, above cited. 

443. The Differential Method. — This, the method which 
has principally proved successful thus far, consists in meas- 
uring the annual displacement of the star whose parallax we 
are seeking, with respect to other small stars near it in appar- 
ent position {i.e., within a few minutes of arc), but presumably 
so far beyond as to have no sensible parallax of their own. 

If, for instance, the observer notes the apparent place of an 
object at no great distance from him with reference to the 
trees on a distant hillside, and then moves a few feet one way 



396 APPENDIX 

or the other, he will see that the nearer object shifts its posi- 
tion with reference to the trees. In the same way, on account 
of the earth's orbital motion, those stars which are very near 
the earth appear every year to shift slightly backwards and 
forwards with respect to those that are far beyond them ; and 
by measuring the amount of this shift it is possible to deduce 
approximately the parallax and distance of the nearer stars. 

We say approximately, because the shift thus measured is 
not really the whole parallax of the nearer star, but only 
the difference between that parallax and the parallax of the 
remote objects with which it is compared ; so that observa- 
tions, if accurately made, will always give us for the nearer 
star a parallax too small, if anything, — never too large ; and, 
as a consequence, the distance of the nearer star determined 
in this way will come out a little too large, and never too 
small. 

444. The necessary measurements, if the comparison stars 
are within a minute or two of arc, may be made with the filar 
micrometer (Sec. 415); but if the distance exceeds a few min- 
utes, we must resort to the " lieliometer " (see General Astron- 
omy, Art. 677) with which Bessel first succeeded ; or we may 
employ photography, which the late Professor Pritchard at 
Oxford and others still more recently have done with con- 
siderable success. 

On the whole, the differential method, notwithstanding the 
fundamental objection to it that it never gives us the entire 
parallax of the star, is at present more trustworthy than the 
other. 

It is obviously necessary to choose for observation by either 
method those stars that are presumably near us. The most 
important indication of the nearness of a star is a large proper 
motion ; brightness, also, is of course confirmatory. Still, 
neither of these indications is certain. A star which happens 
to be moving directly towards or from us shows no proper 



STELLAR PARALLAX 397 

motion at all, however near it may be ; and the faint stars 
are so very much more numerous than the brighter ones that 
among their millions it is quite likely that we shall ultimately 
find individuals which are even nearer than Alpha Centauri. 

445. Spectroscopic Method. — In time it will be possible to 
determine the distance of certain binary stars by the help of 
the spectroscope. The velocity of one or both of the two 
stars " in the line of sight " can be measured by the spectro- 
scope at different parts of the star's orbit, and this will enable 
us to compute the size of the orbit in miles when we know its 
period and its inclination to the line of sight ; at the same 
time the micrometer measures will give its angular dimen- 
sions, and from these data the distance can be found. It will 
probably be many years, however, before any results can be 
obtained in this way, because the periods of most of the 
binaries are very long. 



SUGGESTIVE QUESTIONS 

FOR USE IN REVIEWS 



To many of these questions direct answers will not be 
found in the book ; but the principles upon which the answers 
depend have been given and the student will have to use his 
own thinking in order to make the proper application. 

1. What point in the celestial sphere has both its right ascen- 
sion and declination zero? 

2. What angle does the (celestial) equator make with the hori- 
zon at this place ? 

3. Name the (fourteen) principal points in the celestial sphere 
(zenith, etc.). 

4. What important circles in the heavens have no correlatives 
on the surface of the earth ? 

5. What constellation of the zodiac rises at sunset to-day, and 
which one is then on the meridian? (Use the star-maps.) 

6. If Vega comes to the meridian at 8 o'clock to-night, at what 
time (approximately) will it transit eight days hence ? 

7. What bright stars can I observe on the meridian between 
4 and 5 p.m., in the middle of August ? (See star -maps.) 

8. At what time of the year will Sirius be on the meridian at 
midnight ? 

9. The declination of Vega is 38° 41'; does it pass the meridian 
north of your zenith, or south of it? 

10. What are the right ascension and declination of the north 
pole of the ecliptic ? 

11. What are the longitude and latitude (celestial) of the north 
celestial pole (the one near the Pole-star) ? 

12. Can the sun ever be directly overhead where you live ? If 
not, why not ? 

13. What is the zenith distance of the sun at noon on June 22 
in New York City (lat. 40° 42') ? 

14. What are the greatest and least angles made at New York 
by the ecliptic with the horizon at their point of intersection ? Why 
does the angle vary ? 



SUGGESTIVE QUESTIONS 399 

15. If the obliquity of the ecliptic were 30°, how wide would the 
temperate zone be? How wide if the obliquity were 50°? What 
must the obliquity be to make the two temperate zones each as wide 
as the torrid zone ? 

16. Does the equinox always occur on the same days of March and 
September ? If not, wmy not ; and how much can the date vary ? 

17. Was the sun's declination at noon on March 10, 1900, pre- 
cisely the same as on the same date in 1903? 

18. In what season of the year is New Year's Day in Chili ? 

19. When the sun is in the constellation Taurus, in what sign of 
the zodiac is he ? 

20. In what constellation is the sun when he is vertically over the 
tropic of Cancer? Near what star? (See star-map.) 

21. When are day and night most unequal ? 

22. In what part of the earth are the days longest on March 20 ? 
On June 20 ? On December 20 ? 

23. Why is it warmest in the United States when the earth is 
farthest from the sun ? 

24. W^hat was the Russian date corresponding to Feb. 28, 1900, 
of our calendar ? To May 28 ? 

25. Why are the intervals from sunrise to noon and from noon to 
sunset usually unequal as given in the almanac ? (For example, see 
Feb. 20 and Nov. 20.) 

26. If the earth were to shrink to half its present diameter, what 
would be its mean density ? 

27. Is it absolutely necessary, as often stated, to know the diam- 
eter of the earth in order to find the distance of the sun from the 
earth ? 

28. How will a projectile fired horizontally on the earth deviate 
from the line it would follow if the earth did not rotate on its axis? 

29. If the earth were to contract in diameter, how would the 
weight of bodies on its surface be affected ? 

30. What keeps up the speed of the earth in its motion around 
the sun ? 

31. Why is the sidereal month shorter than the synodic? 

32. Does the moon rise every day of the month ? 

33. If the moon rises at HM5 m Tuesday night, when will it rise 
next? 

34. How many times does the moon turn on its axis in a 
year ? 

35. What determines the direction of the horns of the moon? 

36. Does the earth rise and set for an observer on the moon ? If 
so, at what intervals ? 

37. How do we know that the moon is not self-luminous? 

38. How do we know that there is no water on the moon? 



400 APPENDIX 

39. How much information does the spectroscope give us about 
the moon ? 

40. What conditions must concur to produce a lunar eclipse ? 

41. Can an eclipse of the moon occur in the daytime V 

42. Why can there not be an annular eclipse of the moon ? 

43. Which are most frequent at New York, solar eclipses or lunar? 

44. Can an occupation of Venus by the moon occur during a 
lunar eclipse ? Would an occupation of Jupiter be possible under 
the same circumstances? 

45. Which of the heavenly bodies are not self-luminous? 

46. When is a planet an evening star? 

47. What planets have synodic periods longer than their sidereal 
periods ? 

48. When a planet is at its least distance from the earth, what is 
its apparent motion in right ascension ? 

49. A planet is seen 120° distant from the sun ; is it an inferior 
or a superior planet? 

50. Can there be a transit of Mars across the sun's disk? 

51. When Jupiter is visible in the evening, do the shadows of the 
satellites precede or follow the satellites themselves as they cross the 
planet's disk? 

52. What would be the length of the month if the moon were 
four times as far away as now? (Apply Kepler's third law.) 

53. What is the distance from the sun of an asteroid which has a 
period of eight years? (Kepler's third law.) 

54. Upon what circumstances does the apparent length of a 
comet's tail depend ? 

55. How can the distance of a meteor from the observer, and its 
height above the earth, be determined ? 

56. W r hat heavenly bodies are not included in the solar system? 

57. How do we know that stars are suns? How much is meant 
by the assertion that they are? 

58. Suppose that in attempting to measure the parallax of a bright 
star by the differential method (Sec. 443) it should turn out that the 
small star taken as the point to measure from, and supposed to be far 
beyond the bright one, should really prove to be nearer. How would 
the measures show the fact ? 

59. If Alpha Centauri were to travel straight towards the sun 
with a uniform velocity equal to that of the earth in its orbit, how 
long would the journey take, on the assumption that the star's parallax 
is 0".75? 

60. If A Hair were ten times as distant from us, what would be 
its apparent " magnitude " ? What, if it were a thousand times as 
remote? (See Sees. 346, 347; and remember that the apparent 
brightness varies inversely with the square of the distance.) 



TABLES OF ASTRONOMICAL DATA 

TABLE I — ASTRONOMICAL CONSTANTS 

TIME CONSTANTS 

The sidereal day = 23 h 56 m 4 s .090 of mean solar time. 
The mean solar day = 24 h 3 m 56 s .556 of sidereal time. 
To reduce a time-interval expressed in units of mean solar time to 
units of sidereal time, multiply by 1.00273791; log. of 0.00273791 
= [7.4374191]. 

To reduce a time-interval expressed in units of sidereal time to 
units of mean solar time, multiply by 0.99726957 = (1 - 0.00273043); 
log. 0.00273043 = [7.4362316]. 

Tropical year (Leverrier, reduced to 1900) . 365 d 5 h 48 m 45 s .51. 

365 6 9 8.97. 
365 6 13 48.09. 
29 d 12M4m 2s.864. 
27 7 43 11 .545. 
27 7 43 4 .68. 
27 13 18 37 .44. 
27 5 5 35.81. 



Sidereal year " " " 

Anomalistic year " " " 

Mean synodical month (new moon to new) 
Sidereal month . . 

Tropical month (equinox to equinox) . 
Anomalistic month (perigee to perigee) 
Nodical month (node to node) 



Obliquity of the ecliptic (Newcomb), 

23°27 / 8".26 - 0".468(* - 1900). 

Constant of precession (Newcomb), 

50".248 + 0.000222 (t - 1900). 

Constant of nutation (Peters), 9".223. 

Constant of aberration (Nyren), 20".492 ; (Chandler), 20".521. 



Equatorial semi-diameter of the earth (Clarke's spheroid of 1878), 
-20,926202 feet = 6,378190 meters = 3963.296 miles. 

Polar semi-diameter, 

20,854895 feet = 6,356456 meters = 3949.790 miles. 

Ellipticity, or polar compression (Clarke), 293 \ 46 ; (Harkness), jj— . 

401 



402 



APPENDIX 



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404 



APPENDIX 



TABLE IV — THE PRINCIPAL VARIABLE STARS 

A selection from s. 0. Chandler's oatalogue of variable stars, containing such as, 
at the maximum, are easily visible to the naked eye, have a range Of variation 
exceeding half a magnitude, and can be seen in the United States. 



No. 


Name 


Place, 1900 


Range oi 

Variation 


Period (days) 


Remarks 


a 


8 


1 

2 


K Andromeda? 
o Ceti . . . 


li in 

18.8 
2 14.3 


+ 38° 1' 
- 3 20 


5.6tol3 
1.7 to 9.5 




410.7 
331. G 


< Mir a. Varia- 
tions in length 


3 


p Persei . . 


2 58.7 


+ 38 27 


3.4 to 4.2 




33 ? 


( of period 


4 
5 


|S Persei . . 
a Tauri . . . 


3 1.6 

3 55.1 


4 JO .54 
+ 12 12 


2.3 to 3.5 

3.4 to 4.2 


2 d 
3^ 


20i' 4 8 „, 558.43 
22 h 52™ 12 s 


| Algol. Period 
\ now shortening 
I Algol type, but 
\ irregular 


G 


< Auriga? . . 


4 54. S 


+ 43 41 


3 to 4.5 




Irregular 


7 


a Orionis . . 


5 40.7 


+ 7 23 


0.7 to 1.5 






[rregular 


8 


>/ Geminorum 


I) 8.S 


1-22 32 


3.2 to 4.2 




231.4 




9 


£ Geminorum 


58.2 


+ 20 43 


3.7 to 4.5 


10* 


31, 41m 30.6 




10 


K Canis Maj. . 


7 14.1) 


-10 12 


5.9 to G.7 


1<J 


31. 15m 4G* 


Algol type 


11 


K Leonis . . 


42.2 


+ 11 54 


5.2 to 10 




312.8 




12 


V llydne . . 


10 32.(5 


12 52 


4.5 to G.3 




194.65 




13 


K Hydra? . . 


13 24.2 


-22 40 


3.5 to 5.5 




425.15 


Period short'ing 


11 


t S Libra' . . 


14 55.0 


-87 


5.0 to G.2 


2<i 


7'' 51* 22a.8 


Algol type 


16 


R Corona? . . 


15 44.4 


+ 28 28 


5.8tol3 




[rregular 




16 


K Serpentis 


15 40.1 


+ 15 20 


5.0 to 1:5 




357.0 




17 


a Ilerenlis 


17 10.1 


+ 14 30 


3.1 to 3.9 


Two or three 111011 


ths, but very irreg. 


18 


(JOphiuohi . 


17 11.5 


+ 1 10 


0.0 to 0.7 




20* 7'» 42s.56 




L9 


X Sagittarii . 


17 41.3 


-27 48 


4 to 


7 a 


()i> 17"' 57 s 




*J0 


WSagittarii . 


17 58.0 


- •_':» 35 


5 to (5.5 


7 a 


14<> 16'" 13* 




21 

22 


K Scuti . . . 
Lyra> . . . 


18 42.1 
18 40.4 


- 5 41) 
1 33 i:» 


4.7 to 9 
3.4 to 4.5 


12't 


71.10 
21'' 47- 23s.72 


( Secondary mini- 
] mum about mid- 


23 


\ Cygni . . 


10 40.7 


1 32 40 


4.0 to 13.5 




406.045 


( way 
Period length-ng 


24 


7; Aqnihe . . 


10 47.4 


+ 45 


3.5 to 4.7 


7<» 


4»' 11"' 5D* 




25 


s Sagitta? . . 


10 51.4 


+ 10 22 


5.0 to (5.4 


& 


9'' 11"' 48. 5 




26 


T Vulpecula? . 


20 47.2 


+ 27 52 


5.5 to 0.5 


4a 


10'' 27'" 5(K4 




27 


T Cephel . . 


21 8.2 


■ OS 5 


5.0 to 9.9 




387 




28 


is Cephei . . 


21 40.4 


1 58 i!» 


4 to 6 




430" 




29 


<s Cephei . . 


22 25.4 


• ;,: 54 


3.7 to 4.9 


5<» 


8'' 47'" 39* .3 




30 Pegasi . . 


22 58.9 


1 27 32 


2.2 to 2.7 




Irregular 




31 K Cassiopeia? . 


23 :>:;.."> 


+ 50 50 


4.8 to 12 




429.5 





ASTRONOMICAL DATA 



405 



TABLE V — PROPER MOTIONS AND PARALLAXES 
(Kapteyn, 1901) 



l 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 



20 



a Centauri .... 
LI. 21158 . . . . 
61 Cygni .... 

Sirius 

v' Draconis . . . 
C. Z., V., 243 . . . 
Procyon .... 
Groombridge, 34 . 
Lacaille, 9352 . . 

e Indi 

Arg.-Oeltzen, 17415 
LI. 21258 . . . . 
a Aquilse (Altair) . 
10 Ursse Majoris . 
tj Cassiopeiae . . . 
Arg.-Oeltzen, 10603 
e Eridani .... 
a Lyrae (Vega) . . 
Groombridge, 1830 . 
Polaris 



Mag. 



6.1 
-1.4 
4.9 
8.5 
0.7 
7.9 
7.1 
4.8 
9.0 
8.5 
1.0 
4.2 
3.8 
7.0 
4.4 
0.4 
6.6 



2.1 



Proper 
Motion 



3". 67 
4.75 
5.16 
1.31 
0.16 
8.70 
1.25 
2.80 
7.00 
4.68 
1.27 
4.40 
0.65 
0.50 
1.20 
1.43 
3.03 
0.36 
7.05 



0".045 



Annual 


Distance 


Parallax 


(light-years) 


0".76 


4.3 


0.47 


6.9 


0.41 


8.0 


0.38 


8.6 


0.32 


10.2 


0.32? 


10.2 


0.31 


10.5 


0.30 


10.9 


0.29 


11.1 


0.28 


11.6 


0.25 


13.1 


0.24 


13.6 


0.24 


13.6 


0.20 


16.3 


0.19 


17.2 


0.18 


18.1 


0.16 


20.4 


0.15 


21.7 


0.15? 


21.7 


0".074 


44± 



The above contains with a single intentional exception, one interpolation (No. 6), 
and the addition of Polaris, all the stars on Kapteyn's list having parallaxes exceed- 
ing 0".14. There are about as many more on his list with parallaxes ranging 
between O'.IO and 0M4. 



THE GREEK ALPHABET 



Letteri 


NlllMO 


A, a, 


Alpha. 


B, li 


Beta. 


W A, 


< ..it a. 


A, 8, 


Delta. 


E, «, 


Epsilon. 


7,1 


Zeta. 


II,,, 


Eta. 



Lutton 



(h), o, ,v, Theta. 



1, t, 


[ota. 


K, K, 


Kappa. 


A, A, 


Lambda. 


M, ,4., 


Mu. 


N, r, 


Nil 


S, ft 


\i. 


o, 0, 


Oniicron 


1 1 , 7T, O), 


Pi, 



Letten 


Nam* 


p, ,,, }, 


IMlo. 


Si CT| s, 


Signia. 


T, T, 


Tau. 


Y, „, 


I Fpsilon 


*, </>, 


Phi. 


X, * 


Chi. 


*, i//, 


Pal, 


12, to, 


Oint^a. 



MISCELLANEOUS SYMBOLS 



^ p Conjunction, 
n , Quadrature. 
( v , ( Opposition. 
£2, Asoendihg ffdde. 

'('S, Descending Node 



AIL, or a, Bight Ascension. 
Decl., or ^>, I Inclination. 
A, Longitude (< Selestial). 
/i Latitude (Celestial), 
</>, Latitude (Terrestrial). 



«.>, Angle between line of nodes and line of apsides of an orbit; 

also, sometimes the obliquity ol the ecliptic. 



m 



INDEX 



[All references, unless expressly stated to the contrary, are to sections, 
not to pages.] 



Aberration, of light, 435; determin- 
ing distance of sun, 436. 

Absolute scale of star magnitudes, 
346. 

Acceleration of rotation at the sun's 
equator, 163. 

Achromatic telescope, 406, 407. 

Adams, J. C. (and Leverrier), dis- 
covery of Neptune, 283; orbit of 
the Leonids, 327. 

Aerolite, see Meteorite. 

Age of the sunand planetary system, 
193, 397-399. 

Albedo, denned, 149, 235; of the 
moon (Zollner) , 149 ; of the planets 
(Zollner), 242, 247, 253, 268, 276, 
281, 285. 

Algol, or Beta Persei, 40, 351, 358, 
360. 

Alphabet, the Greek, page 406. 

Altitude, denned, 11 ; parallels of, 
11; of the pole equals latitude, 
80. 

Andromeda, constellation of, 35 ; 
nebula of, 377, 378; temporary 
star in nebula, 355. 

Andromedes, or Bielids, 312, 326, 

Angular measurements, units of, 8. 

Annual or heliocentric parallax, de- 
fined, 343 ; methods of determin- 
ing it for the stars by observation > 
441-444. 



Annular eclipses, 201; nebula in 

Lyra, 378, 382. 
Anomalistic year, 127. 
Anomalous phenomena in comets, 

308. 
Apex of the sun's way, 342. 
Aphelion defined, 120. 
Apogee defined, 137. 
Apparent motion of a planet, 225- 

229; motion of the sun, 115-117; 

solar time, 88. 
Apsides, line of, defined, 120, 137 ; of 

the moon's orbit, 137. 
Aquarius, 78, 118. 
Aquila, 71. 
Arcs, of meridian, measurement of, 

105, 110. 
Areas, equal, law of, 121, 137, 220. 
Argo Navis, 51. 

Ariel, a satellite of Uranus, 252. 
Aries, first of, defined, 17 ; constel- 
lation of, 38, 118. 
Asteroids, or minor planets, 260-263. 
Astronomical constants, table of, 

Table I, page 401 ; day, beginning 

of, 90; symbols, page 406; unit, 

see Distance of the sun. 
Astronomy, utility of, 1. 
Atmosphere of the moon, 148; of 

Mars, 253; of Mercury, 242; of 

Venus, 248. 
Attraction of gravitation, its law,, 

220, 221. 



407 



408 



LESSONS IN ASTRONOMY 



Auriga, 41. 

Axis of the earth, 13, 109 ; motions 

of, 109. 
Azimuth defined, 11. 

B 

Barnard, E. E., measures of diam- 
eters of planets, 262, 267, 275, 285 ; 
seasonal changes on Mars, 256; 
discovery of fifth satellite of Ju- 
piter, 272; of comet by photog- 
raphy, 314* ; photograph of Swift's 
comet, 314*. 

Bayer, J., his system of lettering 
the stars, 24. 

Beginning of the century, 130; of 
the day, 90, 98. 

Bessel, F. W., dark stars, 350, 360 ; 
first measures stellar parallax, 
441, 444. 

Bethlehem, the star of, 355. 

Biela's comet, 311, 312. 

Bielids, or Andromedes, 312, 324, 328. 

Binarystars, 368-371 ; spectroscopic, 
373, 374. 

Bissextile year, 129. 

Bode, J. E., his law of planetary 
distances, 219. 

Bond, W. C, discovery of the 
" gauze ring" of Saturn, 277; 
discovery of Hyperion, 280. 

Bootes, 59. 

Boys, C. V., determination of the 
constant of gravitation and of the 
density of the earth, 113. 

Bredichin, Th., his theory of 
comets' tails, 307. 

Brightness, of comets, 291; of me- 
teors, 318 ; of stars, and causes of 
difference, 345-350. 

Brooks, W., his comets, 290, 299. 



CjESAr, Julius, reformation of the 
calendar, 129. 



Calcium, in the sun, 176 ; in faculae, 
165; in chromosphere and prom- 
inences, 182, 182*. 

Calendar, the, 128-130. 

Calory, the, defined, 187. 

Camelopardus, 31. 

Campbell, W. W., spectrum of 
Mars, 253 ; radial motion of stars, 
341 ; spectra of nebulous stars, 380. 

Canals of Mars, 256. 

Cancer, 52, 118. 

Canes Venatici, 58. 

Can is Major, 49. 

Canis Minor, 48. 

Capricornus, 73, 118. 

Capture theory of comets, 298. 

Cardinal points defined, 16. 

Carrington, R., discovery of the 
peculiar law of the sun's rotation, 
163. 

Cassini, J. D., discovers division in 
Saturn's ring, 277. 

Cassiopeia, 28; temporary star in, 
355. 

Catalogues of stars, 335. 

Celestial globe, described, 400, 401 ; 
sphere, infinite, 6. 

Centaurus, 62. 

Centrifugal force due to earth's 
rotation, 111. 

Cepheus, 29. 

Ceres, the first of the asteroids, 
260, 262. 

Cetus, 39. 

Chandler, S. C, variation of lati- 
tude, 109 ; investigation of Brooks' 
comet, 1889-V, 299 ; his catalogue 
of variable stars, 361. 

Changes, gradual, in the brightness 
of stars, 353; on the surface of 
the moon, 155. 

Charlois, M., discoverer of aster- 
oids by photography, 260. 

Chemical constitution of the sun, 
175, 176. 



INDEX 



409 



Chromosphere of the sun, 180, 194; 
and prominences made visible by 
the spectroscope, 182; photog- 
raphy of, 182*. 

Chronograph, the, 417. 

Chronometer, the, 417; longitude 
by, 96, 427. 

Circle, meridian, the, 81, 99, 418. 

Circles, hour, defined, 15. 

Circumpolar stars, latitude by, 81. 

Civil day and astronomical day, 90. 

Clark, Alvan, and Sons, makers 
of great telescopes, 412. 

Clark, A. G., discovers companion 
of Sirius, 369. 

Classification of the planets, Hum- 
boldt, 217; of stellar spectra, 
Secchi, 363 ; of variable stars, 352. 

Clock, the astronomical, 417 ; its 
rate and error, 92, 93, 417. 

Clusters of stars, 361, 376. 

Columba, 45. 

Colures defined, 117. 

Coma Berenices, 57. 

Comet, Biela's, 311, 312; Donati's, 
289; Encke's, 293, 311; Lexell- 
Brooks, 299; Halley's, 293; of 
1882, 313, 314. 

Comets, anomalous phenomena 
shown by, 308; attendant com- 
panions, 314 ; brightness and visi- 
bility, 291; capture theory of 
their origin, 298 ; central stripe in 
tail, 308 ; connection with meteors, 
327-329 ; constitution of, 300 ; dan- 
ger from, 310; density of, 303; 
designation and nomenclature, 
290 ; dimensions of, 301 ; elliptic, 
293, 297; envelopes in head, 305; 
families of, 297 ; formation of the 
tail, 306; their light and spectra, 
304; mass of, 302; nature of, 
309; number of, 289; orbits of, 
292, 293; periodic, their origin, 
297, 298; photography of, 314*; 



sheath of comet of 1882, 314; tails 
or trains, 300, 306-308 ; visitors to 
the solar system, 296. 

Comet-groups, 294. 

Conic sections, the, 440. 

Conjunction, defined, 132, 227. 

Constant, solar, defined and dis- 
cussed, 187 ; of the equation of 
light, 432 ; of aberration, 435. 

Constellations, the, 4, 333. (For de- 
tailed description, see Chap. II.) 

Constitution of comets, 300 ; of the 
sun, 194. 

Contraction of a comet nearing the 
sun, 301 ; of the sun, Helmholtz's 
theory, 192, 396, 397. 

Copernicus, rotation of the earth, 
106; his system, 230. 

Corona Borealis, 60. 

Corona, the solar, 183-185. 

Coronium, hypothetical element of 
the corona, 184. 

Correction of error of a timepiece, 
92, 427. 

Corvus, 55. 

Cosmogony, 389-396. 

Crater, 55. 

Cygnus, 68. 



Dark stars, 350, 360. 

Darwin, G. H., motion of the tides, 
211; tidal evolution, 393; demon- 
strates that a meteoric swarm 
behaves like a gaseous nebula, 
394. 

Day, beginning of, 98; civil and 
astronomical, 90. 

Declination, defined, 14; determina- 
tion of, 99, 100; parallels of, 14. 

Degrees of latitude, length of, 110. 

Deimos, a satellite of Mars, 258. 

De l'Isle, J., his method of observ- 
ing a transit of Venus, 437, 438. 

Delphinus, 74. 



410 



LESSONS IN ASTRONOMY 



Density, of comets, 303; of the 
earth, 113; of the moon, 143; of 
the sun, 161. 

Designation and nomenclature of 
comets, 200 ; of the stars, 24, 334 ; 
of variable stars, 361, 

Desl andres, H., photography of 
solar prominences, 182*. 

Diameter of a planet, how deter- 
mined, 232. 

Difference of brightness in stars, its 
causes, 350. 

Diffraction, telescopic, 408. 

Diffraction grating, the, 171, note. 

Dione, a satellite of Saturn, 280. 

Disk, spurious, of a star, 408. 

Displacement of spectrum lines by 
motion in line of sight, 170, 341, 
373. 

Distance, of a body as depending on 
its parallax, 140; of the moon, 
141; of the nebula\ 382; of the 
planets from the sun, Table II, 
page 402; of the stars, 343, 441- 
444; of the sun, by the equation 
of light, 434; of the sun, by aber- 
ration of light, 430; of the sun, 
by its parallax, 437. 

Distribution of the nebula 1 , 382; of 
the stars in the heavens, 384; of 
sun-spots, 169. 

Diurnal or geocentric parallax de- 
fined, 139 ; rotation of the heavens, 
12. 

Doppler, C, his principle, 170, 
341, 373. 

Double stars, 300, 307 ; optical and 
physical, distinguished, 3(17. 

Draco, 30. 

DRAPER, H., photograph of the 
nebula of Orion, 378 ; photographs 
of star spectra, .304. 

I ) n ration of solar eclipses, 203 ; prob- 
able, of the solar system, 193, 
307-300. 



E 






Earth, the, astronomical facts re- 
lating to it, 102; its density, 113; 
dimensions of, 105, 110, Table I, 
page 401 ; ellipticity or oblateness 
determined, 110; its interior con- 
stitution, 114; mass, 113; orbital 
motion of, 115-122, 428; its orbit, 
changes in, 122; its rotation, in- 
variability of, 108; its rotation, 
proofs of, 107 ; shadow of, its 
dimensions, 196; surface area and 
volume, 112; velocity in its orbit, 
158. 

Earth-shine on the moon, 147. 

Ebb defined, 210. 

Eccentricity of the earth's orbit, 
11!); of an ellipse, defined, 119, 
420. 

Eclipses, frequency of, 200 ; of Jupi- 
ter's satellites, 273; lunar, 107- 
100; Oppolzer's canon of, 205; 
number in a year, 200; recur- 
rence of, 207 ; solar, duration of, 
203 ; solar, phenomena of, 204 ; 
solar, varieties of, — total, annu- 
lar, and partial, 201, 202. 

Ecliptic, the, defined, 110 ; obliquity 
of, 110; poles of, 117. 

Elements, chemical, recognized in 
the stars, 302; chemical, recog- 
nized in the sun, 170; of the 
planets' orbits, Table II, page 
402. 

Ellipse, the, defined and described, 
420, 430, 440. 

Elliptic comets, 202, 203. 

Ellipticity, or oblateness of the 
earth, 110. 

Elongation denned, 132, 227. 

Eneeladus, a satellite of Saturn, 
280. 

Encke, J. F., his comet, 203, 311. 

Energy of the solar radiation, 188, 
189. 



INDEX 



411 



Envelopes in the head of a comet, 

.305, 314. 
Equation of light, 431-433; of time, 

89. 
Equator, celestial or equinoctial, 

defined, 14. 
Equatorial acceleration of the sun's 

surface rotation, 163. 
Equatorial telescope, the, 414; its 

use in determining the place of a 

heavenly body, 100. 
Equinoctial, the, or celestial equa- 
tor, defined, 14. 
Equinox, vernal, defined, 17, 116. 
Equinoxes, precession of, 125, 126. 
Equuleus, 75. 
Eridanus, 44. 
Eros, asteroid, 261, 262*. 
Error or correction of a timepiece, 

92, 93, 417. 
Eruptive prominences on the sun, 

182. 
Establishment of a port, 210. 
Eyepieces, telescopic, various forms 

of, 409. 



Faculae, solar, 165. 

Families of comets, 297. 

Faye, H., depth of sun-spots, 168; 
modification of the nebular hy- 
pothesis, 393. 

Filar micrometer, the, 415. 

Fizeau, H. L., the Doppler-Fizeau 
principle, 179 ; measure of velocity 
of light, 434. 

Flood tide, 210. 

Force, repulsive, of light, 306. 

Form of the earth's orbit deter- 
mined, 428. 

Foucault, L. , his pendulum experi- 
ment, 107. 

Fraunhofer, J., lines in the solar 
spectrum, 175, note. 

Frequency of eclipses, 206. 



Galaxy, the, 383. 

Galileo, G., his discovery of Ju- 
piter's satellites, 272 ; discovery of 
phases of Venus, 247 ; discovery 
of Saturn's ring, 277 ; discovery of 
sun-spots, 169; his telescope, 402. 

Galle, J. G., the first to see Nep- 
tune, 283, note. 

Gemination of the canals of Mars, 
256. 

Gemini, 47, 118. 

Genesis of the planetary system, 
390, 391. 

Geocentric parallax, 139. 

Gibbous phase defined, 146. 

Globe, the celestial, described, 400, 
401. 

Grating, diffraction, 171, note. 

Gravitation, 221, 222. 

Gravity, at the moon's surface, 143 ; 
at the pole and equator of the 
earth, 111; at the sun's surface, 
161 ; superficial, of a planet, how 
determined, 233. 

Greek alphabet, the, page 406. 

Gregorian calendar, the, 130. 

Groups, cometary, 294. 

Grus, 79. 

Gyroscope illustrating the cause of 
the seasons, 123. 

H 

H and K lines of calcium, 165, 176, 

182, 182*. 
Habitability of Mars, 259. 
Hale, G. E., photographs of the 

moon, 156 * ; of solar prominences, 

182*. 
Hall, A., discovery of the satellites 

of Mars, 258; mass of Saturn's 

rings, 277. 
Halley, E., discovers the proper 

motion of stars, 339; his periodic 

comet, 293. 



412 



LESSONS m ASTRONOMY 



Harding, C, discovers Juno, 260. 

Harmonic law, Kepler's, 220, 430. 

Harvest and hunter's moons, the, 
136. 

Heat, of meteors, its explanation, 
318; from the moon, 150; from 
the stars, 348, note ; of the sun, 
its constancy, 191 ; of the sun, its 
intensity, 190; of the sun, its 
maintenance, 192 ; of the sun, its 
quantity, 187, 189. 

Heavenly bodies, defined and enu- 
merated, 2; apparent place of, 7. 

Heliocentric or annual parallax, 
defined, 139, 343. 

Helium, hypothetical element in 
the sun, 181 ; its identification 
as a terrestrial element in uran- 
inite, 181 ; in temporary and vari- 
able stars, 355, 356; in nebulae, 
380. 

Helmholtz, H. von, his theory of 
the sun's heat, 192. 

Hencke, L., discovers Astrsea, 260. 

Hercules, 66. 

Herschel, Sir J., illustration of 
the solar system, 238 ; his names 
for the satellites of Saturn and 
Uranus, 280, 282. 

Herschel, Sir W., discovery of 
Uranus, 281 ; his great telescope, 
412; relation between nebulae and 
stars, 395. 

Herschels, the, their star-gauges, 
384. 

Hipparchus, 120, 125, 335, 345. 

Horizon, defined, rational and visi- 
ble, 10. 

Horizontal parallax, 139. 

Hour-angle defined, 422. 

Hour-circles defined, 15. 

Hourly number of meteors, 321. 

Huggins, Sir William, observes 
spectrum of Mars, 253; observes 
spectrum of Mercury, 242 ; ob- 



serves spectrum of nebulae, 380; 
observes spectrum of stars, 362; 
observes spectrum of temporary 
star of 1866, 355 ; spectroscopic 
measures of star motions, 341. 

Humboldt, A. von, his classifica- 
tion of the planets, 217. 

Hunter's moon, the, 136. 

Huyghens, Chr., his discovery of 
Saturn's ring, 277; discovery of 
Titan, 280; invention of the pen- 
dulum clock, 417. 

Hydra, 55. 

Hyperbola, the, 439, 440. 

Hyperion, a satellite of Saturn, 280. 



Iapetus, the remotest satellite of 

Saturn, 280. 
Identification of helium, 181 ; of the 

orbits of certain comets and 

meteors, 328. 
Illuminating power of a telescope, 

405. 
Illumination of the moon's disk 

during a lunar eclipse, 198. 
Illustration of the proportions of 

the solar system, 238. 
Influence of the moon on the earth , 

151; of sun-spots on the earth, 

170. 
Intensity of the sun's heat, 189-190 ; 

of the sun's light, 186. 
Intramercurian planets, 264. 
Invariability of the earth's rotation, 

108 ; of the length of the year and 

distance from the sun, 122. 
Iron in comets, 314 ; in meteorites, 

316 ; in stars, 362 ; in the sun, 175. 



Julian calendar, the, 129. 
Juno, the third asteroid, 260, 262. 
Jupiter (the planet), 266-271; his 
belts, red spot, and other 



INDEX 



413 



markings, 268, 271 ; his rotation, 
270; his satellites, and their 
eclipses, 272, 273. 
Jupiter's family of comets, 297. 



Kant, I., a proposer of the nebular 
hypothesis, 391. 

Keeler, J. E., spectroscopic obser- 
vation of the rings of Saturn, 279 ; 
radial motion of stars, 341 ; types 
of stellar spectra, 363; photo- 
graphs of nebulae, 378; spectra 
and motions of nebulae, 380. 

Kelvin, Lord, formerly Sir Wil- 
liam Thomson, 114, 318, 396. 

Kepler, J., his laws of planetary 
motion, 121, 220, 430. 

Kirchhoff, G. R., fundamental 
principles of spectrum analysis, 
173. 

L 

Lacerta, 76. 

Lagrange, J. L., stability of the 
solar system, 288*. 

Langley, S. P., his value of the 
solar constant, 188. 

Laplace, P. S., his capture theory 
of comets, 298; his nebular hy- 
pothesis, 392, 393; stability of 
the solar system, 288*. 

Lassell, W., his discovery of Ariel 
and Umbriel, 282; his discovery 
of the satellite of Neptune, 286. 

Latitude (celestial) denned, 20; 
(terrestrial) denned, 80 ; length of 
degrees, 110; methods of deter- 
mining, 81, 424, 426; variations 
of, 109. 

Law, Bode's, 219; of the earth's or- 
bital motion, 121 ; of gravitation, 
221, 222. 

Laws, Kepler's, 121, 220, 430. 

Leap year, 129, 130. 

Leo, 53, 118. 



Leo Minor, 54. 

Leonids, the, 324, 325, 326, 329. 

Lepus, 45. 

Leverrier, J. U. (and Adams), 
discovery of Neptune, 283 ; on the 
origin of the Leonids, 329. 

Libra, 61, 118. 

Librations of the moon, 145. 

Lick observatory, telescope, 412; 
various observations, 156, 253, 
256, 262, 267, 272, 275, 299, 314*, 
341, 380. 

Light, aberration of, 435, 436; of 
comets, 291 ; equation of, the, 
432, 433 ; of the moon, 149 ; of the 
sun, its intensity, 186; repulsive 
force of, 306; of the stars, 348- 
350; velocity of, used to deter- 
mine the distance of the sun, 
434, 436; the zodiacal, 265. 

Light-ratio of the scale of stellar 
magnitude, 346. 

Light-year, the, 344. 

Local time, 97 ; time from altitude 
of the sun, 427 ; time by transit- 
instrument, 93, 416. 

Lockyer, Sir J. N., his meteoritic 
hypothesis, 330, 394; on spectra 
of nebulae, 380. 

Longitude and latitude (celestial), 
20; (terrestrial), denned, 94; (ter- 
restrial), methods of determining, 
95, 96, 427. 

Lowell, P., observations on Mer- 
cury, 243*; on Venus, 249; on 
Mars, 256. 

Lunar, see Moon. 

Lupus, 62. 

Lynx, 46. 

Lyra, 67. 

M 

Magnesium, in the sun, 176; in the 

stars, 362. 
Magnifying power of a telescope, 

404. 



414 



LESSONS IN ASTRONOMY 



Magnitudes, star, 345-347 ; star, ab- 
solute scale of, 346; star, and 
telescopic power, 347. 

Mars (the planet), 251-257; habita- 
bility of, 259 ; map of the planet, 
257 ; satellites, 258 ; Schiaparelli's 
observations, etc., 256; telescopic 
aspect, rotation, etc., 253,254. 

Mass, definition, 113; of comets, 
302 ; of earth, 113 ; of moon, 143 ; 
of a planet, how determined, 233 ; 
of shooting-stars, how estimated, 
323; of the sun, 161. 

Masses of binary stars, 371. 

Mazapil, meteorite of, 326. 

Mean and apparent places of stars, 
336 ; and apparent solar time, 88- 
89. 

Mercury (the planet) , 239-244 ; rota- 
tion of, 243 ; transits of, 244. 

Meridian (celestial), denned, 11, 15, 
16; (terrestrial), arcs of, meas- 
ured, 105, 110; circle, the, 81, 99, 
418. 

Meteoritic hypothesis (Lockyer) , 
330, 394; showers, 324-326. 

Meteorite of Mazapil, 326. 

Meteorites, 315 ; their constituents, 
316 ; their fall, 315. 

Meteors, ashes of, 323; connection 
with comets, 327-329; heat and 
light, 318; observation of, 317; 
origin of, 319 ; path and velocity, 
317. 

Michelson, A. A., the velocity of 
light, 436. 

Micrometer, the, 415. 

Midnight sun, the, 86. 

Milky Way, the, 383. 

Mimas, the inner satellite of Saturn, 
280. 

Mira Ceti, 356. 

Missing and new stars, 353. 

Monoceros, 50. 

Month, sidereal and synodic, 133. 



Moon, its albedo, 149; its atmos- 
phere discussed, 148; changes on 
its surface, 155 ; character of its 
surface, 153; density, 143; diam- 
eter, surface area, and bulk, 
142; distance and parallax, 141; 
eclipses of, 195-199 ; heat, 150 ; in- 
fluence on the earth, 151 ; libra- 
tions, 145 ; light and albedo, 149 ; 
maps, 154, 156; mass, density, 
and gravity, 143 ; motion (in gen- 
eral), 132-135; nomenclature of 
objects on surface, 156 ; perturba- 
tions of, 134 ; phases, 146 ; photog- 
raphy of, 156*; rotation, 144; 
shadow of, 200 ; surface structure, 
153; telescopic appearance, 152; 
temperature, 150 ; water not pres- 
ent, 148. 

Motion, apparent diurnal, of the 
heavens, 12, 13; of the moon, 
132-134; of a planet, 225, 226, 
229; of the sun, 115-117; in line 
of sight, or radial motion, effect 
on spectrum, 179, 341, 373, 374; 
of the sun in space, 342. 

Motions of stars, 338-341. 

Mountains, lunar, 153, 156. 

Mounting of a telescope, 414. 

Multiple stars, 375. 



N 






Nadir denned, 10. 

Nadir point of meridian circle, 419. 

Names of planets, 218 ; of satellites 
of the planets, 258, 280, 282, also 
Table III, page 403. 

Neap tide, 210. 

Nebulae, the, 377-382; changes in, 
379; distance and distribution, 
382; drawings and photographs 
of, 378 ; spectra of, 380, 381. 

Nebular hypothesis, the, 392, 393. 

Negative eyepieces, 409. 

Neptune (the planet), 283-287. 



INDEX 



415 



Newcomb, S.,on the age and dura- 
tion of the system, 193; and 
Michelson, the velocity of light, 
436. 

Newton, H. A., estimate of the daily 
number of meteors, 321 ; investi- 
gation of the orbit of the Leonids, 
328 ; nature of comets, 309. 

Newton, Sir Isaac, law of gravi- 
tation, 221, 222. 

Nodes of the moon's orbit and their 
regression, 134 ; of the planetary 
orbits, 224. 

Nordenskiold, A. E. von, ashes 
of meteors, 323. 

Norma, 64. 

Novae, or temporary stars, 355, 355*. 

Number, of comets, 289 ; of eclipses 
in a saros, 207; of eclipses in a 
year, 206 ; of the stars, 332. 



Oases, on Mars, 256. 

Oberon, a satellite of Uranus, 282. 

Oblateness or ellipticity of the 

earth, defined, 110. 
Oblique sphere, 85. 
Obliquity of the ecliptic, 116. 
Olbers, H. W. M., Dr., discovers 

Pallas and Vesta, 260. 
Ophiuchus, 65. 
Oppolzer, Th. von, his canon of 

eclipses, 205. 
Opposition denned, 132, 227. 
Orbit, of the earth, its form, etc., 

115, 122, 428; of the moon, 137: 

parallactic, of a star, 442. 
Orbital motion of the earth, proof 

of, 115. 
Orbits, of binary stars, 370; of 

comets, 292 ; of planets, 223. 
Origin of the asteroids, 263; of 

meteors, 319 ; of periodic comets, 

297. 
Orion, 43; nebula of, 378. 



Palisa, J., discovery of asteroids, 
260. 

Pallas, the second asteroid, 260. 

Parabola, the, 439, 440. 

Parallax, annual or heliocentric, of 
the stars, 139, 343, 441-444 ; diur- 
nal or geocentric, 139 ; solar, by 
transit of Venus, de l'lsle's 
method, 437; of a nebula, 282; 
of stars, 343 ; stellar, how deter- 
mined, 441-444. 

Parallaxes, stellar, table of, Table 
V, page 405. 

Parallel sphere, 84. 

Pegasus, 77. 

Pendulum used to determine earth's 
form, 111 ; Foucault, 107. 

Perigee defined, 137. 

Perihelion defined, 120. 

Periodicity of sun-spots, 169. 

Periods of the planets, 218 ; sidereal 
and synodic, 133, 162, 228. 

Persei, Nova (1901), 355*. 

Perseids, the, 324-326, 328, 329. 

Perseus, 40. 

Perturbations, lunar, 134; plane- 
tary, 122, 288*. 

Peters, C. H. F., asteroid dis- 
coveries, 260. 

Phase of Mars, 253. 

Phases, of Mercury and Venus, 242, 
247 ; of the moon, 146 ; of Saturn's 
rings, 278. 

Phobos, a satellite of Mars, 258. 

Phoebe, name assigned to the sup- 
posed ninth satellite of Saturn, 280. 

Phoenix, 39. 

Photographic power of eclipsed 
moon, 198 ; star charts, 337 ; tele- 
scopes, 337. 

Photographs, of solar prominences, 
182* ; applied to discovery of aster- 
oids, 260 ; of comets, 314* ; of neb- 
ulae, 378 ; of star spectra, 341, 364. 



416 



LESSONS IN ASTRONOMY 



Photography, solar, 104. 
Photometry, stellar, 348, 349. 
Photosphere, the, L65, 104. 
Piazzi, (i., discovers Ceres, 200. 
Pickering, E, C, determination 

of rotation period <>i* Eros by 
photometric observations, 262*; 

photographs <>l" star spectra,, 304, 
373; photometric observations of 
eclipses of Jupiter's satellites, 
433; photometric measures of 

stellar magnitudes, 346. 
Pickering, W. EL, observations on 
moon, 155; on Jupiter's satellites, 
272; announces a ninth satellite 

Of Saturn, 280. 

Pisces, 36, L18. 

Piscis Austral is, 1\). 

Place, of a heavenly body, defined, 

7; of a heavenly body, how deter- 
mined by observation, oo, LOO; <>r 
a, ship, how determined, 42(1, 427. 
Planet, albedo of, defined, 231, 235; 

apparent motion of, 225-221); di- 
ameter and volume, how meas- 
ured, 232; mass and density, how 
determined, 2:1:5; rotation on axis 

determined, 234, 262*J satellite 

system, how Investigated, 2:5b; 
superficial gravity determined, 
2:;:;. 
Planetary data, their relative accu- 
racy, 237 ; system, its genesis, age, 

and duration, 300-308; its stabil- 
ity, 288*. 

Planetoids, see Asteroids. 

Planets, Humboldt's classification, 

217; list of, 218; iutramereurian, 
264; minor, 200-203; possibly 

attending stars, 372; table of 

elements, Table II, page 102; 

table of names, symbols, etc., 

218. 
Pleiades, the, 42, 370. 
Pointers, the, 12, 2(5. 



Pole (celestial), altitude of, equals 
latitude, SO; defined, L3; effect of 
precession, L26; (terrestrial), diur- 
nal phenomena near it, 83; mo- 
tion of, 100. 

Pole-star, former, Alpha Draeonis, 
12(5; how recognized, 12. 

Positive eyepieces, 400. 

Precession of the equinoxes, 125, 
126. 

Pressure, its effect on wave-length 
of Light, 170. 

Prime vertical, the, 11. 

PrOCTOB, R. A., sun-spots, 108. 

Prominences, the solar, 181, 182, 
104. 

Proper motion of stars, 330. 

Ptolemaic system, the, 230. 

Ptolemy, Claudius, 4, 230. 



Quadrature defined, 132, 227. 
Quiescent prominences, 182. 

R 

Radial motion, or motion in line of 
sight, measured by Doppler's 

principle, 170, 341, 373,374. 

Radiant, the, of a meteoric shower, 
324. 

Radius vector de lined, 120. 

Ramsay, W., identification of he- 
lium, 181. 

Rate of a timepiece defined, 417. 

Rectification of a globe, 401. 

Recurrence of eclipses, 207. 

Red spot of Jupiter, 271. 

Reflecting telescope, the, ill, 413. 

Refracting telescope, the, 403-407, 

413. 
Refraction, astronomical, 82. 

Repulsive force of light, 306. 

Reticle, the, 410, 410. 

Retrograde and retrogression de- 
fined, 220. 



INDEX 



417 



Reversing layer, 177. 

Rhea, a satellite of Saturn, 280. 

Right ascension, denned, 18, 93 ; how 
determined by observation, 99, 
100. 

Right sphere, the, 83. 

Rings of Saturn, the, 277-279. 

Roberts, I., photographs of neb- 
ulae, 378. 

Rosse, Lord, heat of the moon, 150 ; 
his great reflector, 412. 

Rotation, apparent diurnal, of the 
heavens, 12 ; definition of, 144 ; dis- 
tinguished from revolution, 100, 
note : of earth, its effect on grav- 
ity, 111 ; of earth, proofs of, 107 ; 
of earth, variability of, 108; of 
the moon, 144 : of the sun, 162, 163. 

Rotation period, of Eros, 262*; of 
Jupiter, 270 ; of Mars, 254 ; of Mer- 
cury, 243 ; of a planet, how ascer- 
tained, 234, 262*; of Saturn, 275; 
of Venus, 249. 



Sagitta, 70. 

Sagittarius, 72, 118. 

Saros, the, 207. 

Satellite system, how investigated, 

236 ; systems, table of, Table III, 

page 403. 
Satellites, of Jupiter, 272 ; of Mars, 

258 ; of Neptune, 286 ; of Saturn, 

280 ; of Uranus, 282. 
Saturn (the planet), 274-280. 
Scale of stellar magnitudes, 346. 
Schiaparelli, G. V., identification 

of cometary and meteoric orbits, 

328; observations of Mars, 256; 

rotation of Mercury and Venus, 

243, 249. 
Schmidt, J., his map of the moon, 

156. 
Schwabe, S. H., discovers perio- 
dicity of sun-spots, 169. 



Scintillation of the stars, 365. 

Scorpio, 63, 118. 

Sea, position of ship at, how found, 

426, 427. 
Seasons, explanation of, 123-124. 
Secchi, A., on stellar spectra, 363; 

on sun-spots, 168. 
Secondary spectrum of achromatic 

object-glass, 407. 
See, T. J. J., measures of planets' 

diameters, 267, 281 ; evolution of 

binary systems, 370. 
Serpens, 65. 
Serpentarius, 65. 
Sextant, the. 420, 421. 
Shadow, of the earth, its dimensions, 

196; of the moon, its dimensions, 

200 ; of the moon, its velocity, 203. 
Ship at sea, determination of its 

position, 426, 427. 
Shooting-stars (see also Meteors), 

320-324 ; ashes of, 323 ; brightness 

of, 323; elevation and path, 322; 

mass of, 323; materials of, 323; 

nature of, 320; number, daily 

and hourly, 321; radiant, 324; 

showers of, 324-326 : spectrum of, 

323; velocity of, 322. 
Showers, meteoric, 324-326. 
Sidereal, and synodic months, 133 ; 

and synodic periods of planets, 

228; time defined, 91; year, 127. 
Signs of the zodiac, 118; effect of 

precession on them, 126. 
Sirius, its companion, 369; light 

compared with that of the sun, 

349 ; its mass compared with that 

of the sun, 370. 
Solar, constant, the, 187 ; parallax, 

158; time, mean and apparent, 

88, 89. 
Solstice defined, 117. 
Sosigenes and the calendar, 129. 
Spectroscope, its principle and con- 
struction, 171, 172: slitle^s, 364, 



418 



LESSONS IN ASTRONOMY 



II. ut, .1 I,. ..!• -,i\, 11., ,.| ii 

p i, .nun. [\\ . L8fl u ltd bo "" i 
in, motion! In line oi light, 178, 

179, ii. ii n i 

:.|>, , 1 1.. ||, ,-|.i, l. iii ii i. . <.o. ., .. |*| I 

,N|mvIi urn. ..I Hi. , In, .in,. |. It, i, mi. I 

1. 1, .mm ,u, , . |H1 .-I , ,-in, ■(■. in 

, n« i il. 01 . ..I lit,- , oiu, I ,.| 

I..-. ;ii. ..i ., „i,,... ■••;. ,.i 

ii, i.tti , iho i of a hoot Inja 

i oi i m m •<•» . the 

aolar, 178 178 oi <i« lolai i oroua, 
im . ,.i , in. pot, 178 

:.p,,liuiu MIIuIvnIn, Ium, I. iiu, u( ii 

,.i m, i,.i, .. I,.; 

:.|>, , ilium ,.| .t i , ll, , l in 1,1,., op,-. 

Ill 

:.|>h, i, . , , l<- ,i nl. (Ii. . (. . ,l,», ii in, ,.( 

iii. o •<» 

i .1 ii i. . < ; . |.« , -iiii.il \.\w oi sun 

,,.« I U.lml,-. !(,'» 

Spoi-,, solnr, n«m< Sun ipot 

:.,..... li.lr ,lolhm,l. '10 

:i il.ilitN ,.| Hi, , .In. ,i.u \ \ -.1.111. 

|88* 
:.i ....I ...I llnio, UT. 

81 u . I.,., ,,N. m :»7l, 878, 11 i 

, .1 ii,- u. .-I . •■> . It n !•- Of, 

, l,.-.l,-.-. Of, 181, •-«• .i.uk. 

iO ttlQ .i. i ii n I,-. i in. i ii, -in, ii 
.im..,. 'i i , I... i, I.-. i, -ii-. ,.i. 
881, m dlat "..,- of, i •. ii 
distribution of, KM . doublet, •<•<.. 

oO, ■ i iv n .. ..-ii im, mi- Ih, in. 

ll, .1 ll.M.l 111,-.... 

i ■• QOtl 1' I" Ol ' - ' > >'u .slurs 
, ,mi.|. u, ,1 \> ill. -.mill- It. . I'v l'» 
lUIU'.iniu.l,". in. I Im i- In u, ■-. I I | 

m. in ...i,l ipp ...in |>1 i, 
mi in in. I u, w . ft8 j mo 
HOD I ' u.nll.,. I, 

Oty . |0 I, I 18, ft .-♦ unml.m of, 

,.., ,11 ,v Of, H t, HI I" 
I ,1-1, \ . .: 10 • l>.'.M ill 

Ihootiiij I i\ rtao Mt>V i 



p. . I . . -.1 Ml ' •<•! \ I. in Of 

II... 18(1 I. ...,.,.,.., N 

total n.i. Mini ..i light ii iim, 

1 1 twinkling ,.(. .... yariftblft, 

Mil , I «i'i. l\ . /•.<„■ ioi 

SI. ii iii , ,-i till I I. i . Ii, I I, 

M..I. i.i. .1 -, lout amount 

:>t< II n p.. .Ml. i s, .. i.ii.l, of, l.il.l,- 

\ . /•..■. LOO |»h,. I, .in, !. j 
Slrurlui.- ,,| (lie .l.ll.n hum 

:< i i.i \ . . ii mi. oi Satui " ■■• 

i hi , \ , in, i in, ,.| \< plum-. 

■Mill. !• , .111,1 ,llll.,ll,Ul Of, I'' 1 . 

'.*>, , :•»'. .i|.|. ii, in moli, mi in llm 

In i\ . ii . I I > I I , . il | , lll.MllO 

pli, «, . 180 Itl I Oil million. I'M . 

Iti oorona, 188 188; Itl dow ItQ . 

lot . .Inn, -m. mm. ,.1. I(.0 ,li-.l in, , 

of, 188, 150, i 14 i IH ,i, ..,,..(, 
i,-, ..••i.i ,,i in ii. i ,(. i i, i.i.r. ii, . 

I l\ ll\ ,MI It'. Ill I.I, ,'. Il.l llMlll 

Of, Quantity . mlrm.il \ , iii.l 1. 1. un 

i,.....,, r>, !"• light of, Un 

in i, ii ii n . im. hi i "i . 1(1] . mo 

lion in p ... I ' |. u .ill. i\ ol. 

180, i i i 18 pio.,...., ..,,-.. 181, 

l'»l ., \ , i in- l.i\,-i . llm, 

i, , i"i rotation of, 1(19 IW 

l>, , l i un, Of, I I '. I I • . l» mponi 
Im, Of, UK) i, i.i|>,..iiui, .liiuin 

lahlng, i "«K\ <m . >•►<.. uoi,- 

Niiii -|>ol ., ippo.ll.iu, , in.l li.iluiv, 

in... i ,o , .,,, ., ,.i Ki8 diatrlbu 

lion ol. l(.'» S|.,.,i,i -. \a\\ ol 

latitude, io'» Miiiii.-n. , ,^\ iim 

, Mill 1,0 ,., llO.ll, ll> Ol. »<>'> 

p, . n um ol . I , '. 
Su|>,>i I., .il •! i\ n \ ol i |.l. in, I . how 

,l,l,i in. \\{ 
Nm. I i. , i . mini.- ol (Im moon. 1 Q |, 

I.I 

'Ml ll 111.. Ill, (, VI I, . .> ' I I '*' 



INDEX 



419 



Synodic and sidereal months, 133; 
and sidereal periods of planets, 

228. 

m, planetary, its age and 'Jura- 
tion, 397-309; its genesis and 

Jution, 390 stability, 

288*; stellar, its probable nature, 
385-388. 

Syzygy defined, 132. 

T 

Tables: astronomical constants, 

Table I, page 40 1 ; astronomical 

mbols, p a g t 406 ; b i 1 1 a r v 1 1 a. r 1 . 
orbits and m 70; Bode's 

law, ^19: constellations, show- 
ing plaee in heavens, page 
Greek alphabet, page 408; moon, 

name-, oi principal objects, 155; 

planets elements, Table JJ. nopv 
402 : pi a n e 1 1 ' n a. mes, d i 1 1 a. n < ; e I . 
etc*, approximate dlite 

ems, Table III, f*g£g 403: 
stellar parallaxes arid proper mo- 
tions, Table V f page 405: variable 
J abk IV, pag<i 404. 
of cornets, 390, 301, 306 

Taurti 

Telegraph, longitude by, 05. 

ope ; achromatic, #06, 407; 

I of, 109; general prin- 
ciples of, 102 illuminating power, 
400 • magnifying power, 404 ; mag- 
nitude of stars visible with a 
:. 347 : mounting/ of, 
414: reflecting; 411; simple re- 
fracting, 40':;. 
Telescope-, great, 412. 

his cornet, 389, 330, 
Temperature of the moon, 150; of 

the sun, 190. 
Tempore; 

Terminator, the, defined and de- 
icrfbed, ho 



Tethys, a satellite of Saturn, 280, 
Thomsojt, Bis w. (now j.orjj 

Kklvjn;, internal heat of the 

earth, 598 : beat of meteors, 318; 

rigidity of the earth, 1 1J. 

Tidal wave, conrse of, 2\.'>. 

'J ides, definitions relating to, 210; 
due mainly to moon's action, 209; 
explanation of, 204, 309, 21] , 212; 
height of, 214: in rive/s, 215 
motion of, l\ 1, 213, 

Time, equation of, 89; local, from 

sun'- altitude, \ll . methods of 
determining. 92, 93, 427. /elation 

to bonr-angle, 132 -. de- 

fined, 01: solar — mean and aj>- 
parent, 88, 89; standard, defined, 

. satellite oi .Saturn, 240. 

mia, satellite of UraB 

Total and annular eclipse », 197 

201. 

DJ of meteors, 315, 
Transit or meridian circle, 41, 99, 
418. 

Transit-instrument, the, 02, 410. 

Transits, of Mei 
250, 

Triangulum, 'M. 

'I ropical year, the, 127. 

.kling of the stars, 305, 
'Iv.HO BKAHK, iiis temporary 

in Cassiopeia, 355, 



Ultra-Neptunian planet. ! 
L'mbriel, a. satellite of L'ranus, 

stellar, its structure 
L'ranographv defined 
UranoJite, see Mete. 
Unmu 'the planet;, 281, 288 

Minor, 27. 

Utility oi . , 1 



420 



LESSONS IN ASTRONOMY 



Vanishing point, 6, note. 

Variable stars, 352-361; in star 
clusters, 361 ; table of, Table IV, 
page 404. 

Velocity, of earth in its orbit, 102, 
158; of light, 436; of moon's 
shadow, 203; of meteors and 
shooting-stars, 317, 322; of star 
motions, 340, 341. 

Venus (the planet) , 245-250 ; phases 
of, 247 ; transits of, 250. 

Vernal equinox, the, 17, 36, 116. 

Vertical circles, 11. 

Very, F. W., measures of lunar 
heat, 150. 

Vesta, the fourth asteroid, 260. 

Virgo, 56, 118. 

Visible horizon denned, 10. 

Vogel, H. C, spectroscopic deter- 
mination of star motions in the 
line of sight, 341 ; spectroscopic 
observations of Algol, Spica, and 
Mizar, 360, 373, 374. 

Volcanoes on the moon, 153. 

Vulcan, the hypothetical intramer- 
curian planet, 264. 

Vulpecula, 69. 

W 

Water absent from the moon, 148. 
Wave-length of a light-ray affected 
by motion in the line of sight, 



Doppler's principle, 179, 341; 

affected by pressure, 179. 
Wave, tidal, its course, 213. 
Way, the sun's, 342. 
Weather, the moon's influence on, 

151. 
Weight, loss of, between pole and 

equator, 111. 
Wilson and Gray, temperature of 

the sun, 190. 
Wolf, Max, introduces photo- 
graphic method of discovering 

asteroids, 260. 
Wolf, R., sun-spot curve, 169. 



Year, the sidereal, tropical, and 
anomalistic, 127, and Table T, 
page 401. 

Z 

Zenith, the, defined, 10. 

Zenith distance defined, 11. 

Zero points of the meridian circle, 

418, 419. 
Zodiac, the, and its signs, 118; its 

signs as affected by precession, 

126. 
Zodiacal light, the, 265. 
Zollner, J. C. F., determination 

of planet's albedoes, 242, 247, 253, 

268, 276, 281, 285; measurement 

of moonlight, 149; measures of 

light of stars, 348. 



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